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%h$& k % goarb of frofessors of h fUM College of P». 



TREATISE 



HARMONY 



TRANSLATED AND ADAPTED FROM THE GERMAN OF 

ERNST FRIEDRICH EICHTER 

(PROFESSOB AT THE C N SEE V ATO EI UM OF MUSIC, LEIPZIG), 

BY 

FRANKLIN TAYLOR. 



LONDON 
PUBLISHED BY J. B. CRAMER AND CO., 201, REGENT STREET, W. 



LONDON '. 

SWIFT AND CO., REGENT PRESS, KINQ STREET, 

REGENT STREET, W. 



PREFACE. 



This work is an adaptation of the Text- book in use at the Leipzig 
Conservatoriuni of Music — the " Lehrbuch der Harnionie," by Ernst 
F. Bichter, Professor at the Conservatorium, and Musical Director of 
the University of Leipzig. Having found, by personal experience, 
that the .above work not only contains much that is new in its 
manner of treating certain subjects, but moreover is based upon 
a more complete and practical system than any other course of har- 
mony with which I am acquainted, it occurred to me while pursuing 
my studies at Leipzig that a literal translation of it into the English 
language would be acceptable to English students and teachers, and 
might occupy a similar position in England to that which the original 
has for some years held in Germany. 

In the course of my labour, however, I have found that certain 
slight alterations and omissions might be effected with advantage to 
the practical employment of the work. These alterations I have 
endeavoured to carry out conscientiously, and to the best of my 
ability ; and the result is the book in its present form. 

It differs from the original in the following particulars : — 

Firstly. — The progressive order of the book with regard to difficulty 
has been slightly modified, with a view to the avoidance of all ex- 
planatory matter not immediately bearing upon the subject in hand. 



IV PREFACE. 

Secondly. — The chapters on Elaboration of Melody and of Accom- 
paniment, and on the Harmonic Phrase in two, three, five, six, seven, 
and eight parts, have been omitted, as belonging rather to the study 
of Counterpoint than that of Harmony. 

Thirdly. — Certain subjects which in the original appear to be 
inadequately explained, or even not mentioned, but which are never- 
theless essential to the completeness of the work, have here been 
enlarged upon ; and several new examples and exercises, as well as 
marginal notes for reference, have been added for the better illustra- 
tion of the various chapters. 

With these exceptions, the present work is a nearly literal trans- 
lation of the original. 

I purpose to follow this treatise by a second, on " Counterpoint 
and Fugue," which shall contain those chapters of the " Lehrbuch 
der Harmonie " which have been omitted in the present work, and 
also a translation of the "Lehrbuch der Fuge," by the same 
author. 

In conclusion I have to express my thanks to Mr. E. J. Hopkins, 
organist of the Temple, for his kind advice and assistance during the 
progress of my work, as well as for many very valuable suggestions. 

London, November, 1864. 



INTRODUCTION. 



OF SCALES. 

Between any two different sounds a certain difference of pitch must necessarily 
exist ; this difference, which may be greater or less according as the sounds are 
more or less distant from each other, is called an interval. 

The smallest interval employed in harmonic combinations is termed a 
semitone. 

Semitones are called diatonic when they occur between two sounds of 
different names, chromatic when they are formed by the chromatic alteration 
of any one sound. 

Diatonic semitones. Chromatic semitones. 

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P 



231 



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3te 



The interval next hi size to a semitone is called a tone, and contains two 
semitones. 

A succession of sounds arranged in alphabetical order and extending to the 
repetition or octave of the first note, thus — A B C D E F G A — is called a 
diatonic, scale. 

Formerly, diatonic scales were formed starting from each of the above sounds 
(except B) ; at the present time, however, two are found sufficient, viz., those 
commencing on C and on A. 

The diatonic scale commencing on the note C is called the major scale, or the 
scale in the major mode ; and the! sounds of which it is composed are termed the 
degrees of that scale, the lowest being called the first degree, the next above it the Degrees of 

t ■, -, the scale. 

second degree, and so on. 

If we examine the intervals which separate the different degrees of the major Place of tha 
scale, we find semitones between the third and fourth, and between the seventh aemltones. 
and eighth degrees, and tones between all other degrees. This will be evident 
from the following example, in which the tones separating the different degrees 
are divided into two semitones by means of the black notes ; the intervals between 
the third and fourth and the seventh and eighth degrees do not, however, admit 
of such division (since for all practical purposes E $ is identical with F, and B J 
with C) : these intervals are therefore semitones. 

1 2 34 5 6 78 



1 



f~TL ~~--i^7^^^ 



— J Semitone. Tone. Tone. 

-— ' Tone. 

Tone. 



LNTKODUCT10N. 



Major scales 
in different 
keys. 



Chromatic 
alteration of 
the seventh 
degree. 



Minor scale. 



A major scale may then be described as one in which the semitones fall 
between the third and fourth, and seventh and eighth degrees. 

If be taken for the first degree of the major scale, the natural alphabetical 
succession of notes will, as has been shown, form a correct major scale ; if, 
however, any other note be employed as the first degree, a chromatic alteration of 
one or more notes will be found necessary to preserve the correct order of tones 
and semitones. Thus, in the scale of G major, the natural order of notes would 
give a tone between the seventh and eighth, and a semitone between the sixth 
and seventh degrees, as will be seen from the following example : — 



Chromatic 
alteration of 
the sixth and 
seventh 
degrees of the 
minor scale. 



Alterations 
omitted in 
descending. 



i 



9 



6 
IZ2I 



7 



Tone. Tone. Semitone. Tone. Tone. Semitone. Tone. 

It will, therefore, be necessary to raise the seventh degree chromatically, in 
order to bring it nearer to the eighth, from which it will then be separated by a 
semitone only, thus : — 

1 2 3 4-5 6 



P 



-A, 



8 



IZ2I 



Tone. Tone. Semitone. Tone. Tone. Tone. Semitone. 

The diatonic scale commencing on the note A, is called the minor scale, or 
the scale in the minor mode. If formed of the natural alphabetical succession 
of notes the semitones will be found between the second and third, and the fifth 
and sixth degrees, as in the following example : — 

12345678 



P 



7Z2I 



Tone. 



Tone. 



Semitone. Tone. 



Tone. 



Tone. Semitone. 

This is the normal minor scale. For reasons which will be hereafter 
explained (see p. 23) it has been found necessary to alter the sixth and 
seventh degrees, by raising them chromatically one semitone. The ordinary 
form of the minor scale at the present day is therefore as follows : — 
12345678 



I 



wm 



"Cr 



"23" 



!!=§ 



Tone. Semitone. 



Tone. Semitone. 

In the descending scale, the chromatic alterations are usually omitted, and the 
scale appears in its original form. On this account the alterations are always 
accidental, i. e., they are not expressed in the signature. 

87654321 



i 



§M==*SEE.te 



Tone. 



Tone. Semitone. L 



Tone. 



Semltone. ■— 



Tone 



INTRODUCTION. 



The signature of the scale of A minor will therefore be the same as that of Signature of 
C major, namely, it will require neither sharps nor flats. Bca l e- 

A minor scale which bears the same signature as any given major scale is Relative 
termed the relative minor of that scale, which is also called the relative major of 
the minor scale. 

The first degree of a minor scale is always the sixth degree of its relative 
major ; thus, in the foregoing examples, A will be found to be the sixth degree of 
the scale of C ; A is therefore the relative minor of C. This will at once be 
seen if we compare the relative major and minor scales : — 



C major: 

A minor: 
Or expressed in notes — 



12346678 

CDEFGABC 



ABCDEPfGfA 



t 



¥ 



T=C 



2 



4 



#^ 



The same rule applies to scales commencing on any note whatsoever; thus, 
the relative minor scale of G major will have for its first degree the sixth degree 
of the scale of G major (namely, E), and will bear the same signature as that 
scale. 

1234567 8 

Scale of G major: GABCDEFfG 



3 4 5 6 



Scale of E minor : 



E F| G A B Cf Df E 



A scale composed entirely of semitones, as in the following example, is termed Chromafcio 

7 .. 7 Bcale. 

a chromatic scale. 



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res: 



OF INTEEVALS. 

The distance which separates any two sounds is reckoned by diatonic degrees, 
and the interval formed by those sounds is named accordingly. Thus, if G be 
the lower note, and considered as the first degree, A will be the second degree, 
and the interval G-A will be that of a second. E will be on the sixth degree, 
and the interval G-E will therefore be a sixth, &c. 



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etc. 



INTRODUCTION. 



Counting then always from the lower note or first degree, and employing all 
the notes of the scale as upper sounds, the following intervals will be found : — 



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oo" -ef^ -&>- -<S>- -rS^ -IS 1 - -&- -&- 

Unison. Second. Third. Fourth. Fifth. Sixth. Seventh. Octave. 

The intervals are generally only counted as far as the octave, the same order 
being repeated for those intervals which he beyond that compass ; thus the ninth 
degree is considered as the second, the tenth as the third, and so on. 

There are, however, reasons which will be perceived hereafter for giving 
names also to those intervals which are greater than the octave. All such will 
therefore have two names, as follows : — 

m , m Fourteenth. Fifteenth. 
_ Twelfth. Thirteenth. _ -«- 
Octave. Ninth. Tenth. Eleventh. -^- -C2- -SZ 
^3 c^ 



i 



¥ 



zz: 



Octave. Second. Third. Fourth. Fifth. Sixth. Seventh. Octave. 

It will be seen that the above series of intervals is composed entirely of the 
notes of the diatonic major scale, and has always the first degree of that scale 
for the lower note of each interval. It is, however, easy to understand that any 
other degree of the scale would serve as the lower note of an interval, in which 
case the numbers of the two sounds forming the interval will be changed (inas- 
much as the lower note of an interval is always considered as the first degree), 
and other slight differences will occur. 

Classification In order to obtain a clear insight into these differences, the following principles 

of intervals. must be borne in mm( j ._ 

(a) The above series of intervals, in which the lower note is the first 
degree of a major scale, while all the other degrees of the scale are employed 
as upper notes, serves as the foundation of all intervals. 

(b) All the intervals therein contained are termed major, and some of 
them perfect. 

(e) Any chromatic alteration of either of the two notes which form an 
interval alters neither the numbers of the degree, nor the name of the 
interval, but necessitates a more exact definition. If, for example, a sharp 
or flat be added to either of the notes forming the fifth, G-C, it remains a 
fifth still, but is evidently a very different fifth from what it originally was. 



P 



fe=fe 



In order then to distinguish between the various chromatic alterations of 
intervals, the following nomenclature is used : — 



INTRODUCTION. 



(1) Unisons, fifths, fourths, and octaves, which are formed of the notes 
of the diatonic major scale, and having the first degree of the scale for the 
lower note, are called perfect. All other intervals of the same scale are 
called major. 



-1 




Perfect. 


Major. 


Major. 


Perfect. 


Perfect 


Major. 


Major. 


Perfect. 


Major. 


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f( 


\ 












CJ 








V 


z 








rj 












i) 




-&&- 


-&CJ 


-S- 


-*5>- 


-«- 


-<S>- 


-<S- 


-Si- 


-S>- 



Unison. Second. Third. Fourth. Fifth. Sixth. Seventh. Octave. Ninth. 

(2) If the upper note of a major interval be chromatically lowered one 
semitone, a minor interval is formed. 



Minor. Minor. Minor. Minor. Minor. 



i: 



w ^ feg- - 



Second. Third. Sixth. Seventh. Ninth. 



Other kinds of intervals may be formed by various other chromatic altera- 
tions ; of these, however, it will not be necessary to speak at present. 

Those which have already been mentioned may be classified as follows : — 



I 



Unison. 
Perfect. 



Seconds. 

Major. Minor. 



Thirds. 

Major. Minor. 



Fourth. 

Perfect. 



w 



^ 



& 



ZE 



i 



Fifth. 
Perfect. 



Srxths. 
Major. Minor. 



Sevenths. 
Major. Minor. 



Octave. 
Perfect 



w 



ffi 



DIVISION OF INTEEVALS INTO CONSONANT AND DISSONANT. 

By the expression consonant and dissonant intervals we do not understand 
such as do or do not sound well, as the terms might seem to imply, but by the 
former is meant those which when heard produce a final and complete effect on 
the ear by themselves, and by the latter those which recpiire to be followed by 
another harmony, without which their effect would be unsatisfactory and 
incomplete. 

Of those intervals with which we are already acquainted, the perfect intervals, Consonant 
and the major and minor sixths and thirds are consonances ; the unison, perfect ^tervaU n * U 
fifth, and octave are also termed perfect, and the thirds and sixths imperfect 
consonances, as the effect of the former is the more complete of the two ; the 
major and minor seconds and sevenths are dissonances. 



INTRODUCTION. 



INVEESION OF INTERVALS. 



As has already been shown, the interval is usually counted upward from the 
lower note ; should there be reasons, however, for reversing this principle and 
counting downwards from the upper note, it is always necessary to express this 
deviation from rule by saying a fifth lower, a sixth lower, &c. Thus we should 
say — D is the fifth of G, G is a fifth lower than D, or a fifth below D. 



1 



W 



It will readily be seen that the interval itself is unaltered by this proceeding. 
Inversion of It is, however, otherwise, when the upper note of an interval is transposed an 

octave lower, and consequently below the note which was originally lowest. If, 
for example, the upper note D of the fifth G-D be transposed an octave lower, 
the interval will not remain unchanged, but will become a fourth, D-G. 

5 4 



P 



This transposition of the upper note is termed an inversion of the interval. 

By means of inversion, the intervals of the diatonic scale will be altered as 

follows : — 

7 8 

Original Intervals. 1 23 4 5 _|^ J2. ^ 

3?^~ 



m 



r^n rJ-> r*J f-j rj rj r? -^, T^rzr 
*-. « c^ 



Inversions. 8 7 



2Z 



We see, then, that a second becomes by inversion a seventh, a sixth is altered 
to a third, and so on. 

An easy method of finding the inversion of any interval is to subtract the 
sum of the degrees contained in the given interval from the number nine, the 
sum remaining will then give the name of the inversion. 

Thus to find the inversion of a fifth, subtract five from nine, and four 
will remain; the inversion required is therefore a fourth. 

In inverting the various intervals which have hitherto been mentioned we 
find- 
Firstly, that all perfect intervals remain perfect on their inversion ; and 
Secondly, that all major intervals become minor, and all minor intervals 
major. 

The inversions of the intervals already mentioned are as follows : — 



INTRODUCTION. 



Original 
Intervals. 



Their 
Inversions. 




Seconds. 
Major. Minor. 



IT 



Sevenths. 

Minor. Major. 



T^ 



Thirds. 
Major. Minor. 

=fcp 



"g" 



Sixths. 

Minor. Major. 



Fourth. 
Perfect 



-jTXZ 



Fifth. 

Perfect. 



ZZH. 



Fifth. 

Perfect. 



IS2Z 



Fourth. 

Perfect. 



Sixths. 

Major. Minor. 



^ 



Sevenths. 
Major. Minor. 



Thirds. 
Minor. Major. 



a 



rV-^ 



Seconds. 
Minor. Major. 



&■ 



Octave. 

Perfect. 



Unison. 

Perfect. 



rcesi 



An accurate knowledge of the inversions of intervals is not only important for 
the study of double counterpoint, but also because it renders the structure of 
simple harmony much easier, for which reasons the student is earnestly recom- 
mended to master them thoroughly before proceeding farther. 

From the above table of inversions will be seen why the perfect fourth must Perfect fourtl 
be considered as a consonance, notwithstanding that its effect, when heard alone, s °aered°asa 
is far from satisfactory — it is the inversion of a consonance, viz., the perfect fifth, consonance. 
and a consonance can never form a dissonance by inversion. 

All the above inversions are called inversions in the octave, that is, the upper 
note is transposed an octave lower. Other inversions, such as those in the tenth 
and twelfth, which produce quite different results, may be neglected for the 
present, as they have no influence whatever on our immediate studies. 



HARMONY. 



FUNDAMENTAL HARMONIES AND THEIR DERIVATIONS. 

Among the various chords which serve as the harmonic basis of a composition, 
it is easy to distinguish between those which are independent, and those which 
require a connection with preceding and succeeding chords to render them 
intelligible. It is precisely the same difference which has been noticed with 
regard to consonant and dissonant intervals. 

To the first class belong most of the common chords (triads), to the second Fundamental 
the chords of the seventh. These two varieties of chords form the fundamental narmou i eB - 
harmonies from which all others are derived. 



CHAPTER I. 
OF THE COMMON CHORDS OF THE MAJOR SCALE. 



A common chord is formed by a combination of three different sounds (hence Common 
the name triad, which is, however, rarely used). The lowest of these sounds is 
called the root, to which are added the third and fifth — for example : — 




These chords, formed on the roots C, G, and A, show a difference in their 
intervals. While the chords of C and G are formed of major thirds and perfect 
fifths, that of A has a minor third and perfect fifth. 

N.B. — When the word chord is used hereafter the common chord is understood. 

A chord containing a major third and perfect fifth is termed a major chord. Different 
A chord with a minor third and perfect fifth is termed a minor chord. varieties of 

r commOD 

It is of course possible to form a chord on every degree of the diatonic scale, ehords. 
and such chords form the principal harmonic contents of that scale or hey. In 
other words, a composition, in whichever key it may be, will be found to be 
principally composed of the chords which are found on the various degrees of the 
scale of that key. 



10 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



NATUEAL CONNECTION OF THE CHOEDS OP A KEY. 

That chord which is based on the first degree of a scale is the most important, 
since it determines the key. There are, however, others which are nearly related 
and next in importance to it. 

In the natural position of the common chord the root is the first or lowest 
note, and the fifth the highest. The addition of any new interval would either 
alter the chord or double some one of its component parts. 



Chords which 
are nearly 
related to the 
chord on the 
first degree. 



flP^HP 



We have now to find the two chords next in importance to that of the first 
degree, and most closely related to it. These chords must necessarily lie outside 
the compass of the first chord, and yet have some connecting link therewith. 
This link will be found in the extreme boundaries of the chord, namely in C and 
G. G will therefore form the root of the one chord, while C will serve as the 
fifth of the other, the root of which will necessarily be F. 

The relationship of these three chords is distinctly shown in the following 
example : — 



m 



t 



BE 



B 



Names of the 
principal 
common 
chords. 



It will be observed that these three nearly-related chords comprise all the 
notes of the scale. They form the foundation of the key, and must be principally 
employed in practice if the key is to be distinctly recognised. 

On account of their importance they have received special names. The chord 
on the first degree is called the chord of the tonic, that on the fifth degree the 
chord of the dominant, and that on the fourth degree the chord of the sub- 
dominant. Then - place in the scale is as follows : — 



I 



Sub- 
dominant. Dominant. 



V 



s 



ZZ3Z 



-&- 



IV. 



V. 



N.B. — The Roman numerals under the chords signify, and will continue to do so in 
this work, the degrees of the scale on which the root is situated. 



APPLICATION OP THE FOBEGOING HAEMONLES. 

In the application of these three chords we will employ the four-voiced or 
four-part phrase. 
The four-part The four-part phrase consists of four parts or voices, the upper one of which 
is called the soprano, and the lowest the bass ; the next voice under the soprano 



phrase. 



AMPLICATION OF THE FOREGOING HARMONIES. 



11 



is called the alto, and that which is immediately above the bass is called the 
tenor. The soprano and bass are also termed extreme voices, and the two others 
middle voices. 

For the three upper voices separate clefs are employed, which are more 
suitable to their compass than the violin clef (fo. These will be treated of here- 
after. For the present we will not employ a separate stave for each voice, but 
for greater facility in reading the examples, we will make use of two, such as are 
used for pianoforte music, thus : — 



SOPBANO, 

Alto. 




In constructing the four-voiced phrase attention must be paid to two things — 
firstly, to the progression of each voice as considered alone, and secondly, to the 
relationship of each voice to the three others, so that the whole may form what 
is termed pure harmonic progression. 

The application of the three chords already found will afford opportunity for 
several observations and necessitate certain rules and principles. 

As the chord is only composed of three notes, one of these must necessarily be 
doubled when the chord is to be written in four parts. The root is the one 
generally chosen for this purpose, though the others may be doubled, the fifth but 
seldom, and there are cases in which the third cannot be doubled at all. 

As regards the connection of two chords one with another the following rule 
must be observed. 

When any one note is contained in two successive chords it is allowed to 
remain in the same voice. 



I 



a. 




b. 




V 








tk=^= 


^ — 


CJ. 




Or s 




— <s 


CJ 


/iV 






<*J 


[<*)• 








vJ> rj 




r--> 













Rules for 
constructing 
the four-part 
phrase. 



Doubling of 
one of the 
parts of a 
common 
chord. 



Harmonic 
connection of 
two chords. 



In example a, C is a note which is contained in both chords : it is therefore 
retained in the same voice in which it appeared in the first chord, viz., the 
soprano ; in example b, the note G is retained in the alto of both chords. 

The remaining voices proceed to those notes of the following chord which lie 
nearest to them, as in example a, the E in the tenor proceeds to F, and the G of 
the alto to A, &c. 



12 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



Consecutive 
fifths and 
octaves. 



When two consecutive chords are composed of entirely different notes, the 
parts must proceed in such a manner as to avoid what are termed consecutive 
fifths or octaves. 

In order to explain this objectionable progression, which is very apt to occur 
in four-part writing, and on that account cannot be too carefully guarded against, 
we will now proceed to consider 



Different 
kinds of 
motion 
between two 
voices. 



THE KELATION OF ONE VOICE TO ANOTHER AS REGARDS 

PROGRESSION. 

Any two voices may move with respect to each other in three different 
ways, viz. : — 

(1) In similar motion (motus rectus). 

(2) In contrary motion (motus contrarius). 

(3) In oblique motion (motus obliquus). 

When two voices ascend or descend together they are said to move in similar 
motion. 






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:& 



^ 



=£^ 



ZZ±L 



Contrary motion occurs when one voice ascends and the other descends 

J ri , ^—4 



i 



w 



22: 



T 



-&- 



~Sl 



t— r 



~T3- 



In oblique motion one part remains stationary while the other ascends or 
descends. 



m 



9 



T- 



zz: 



^ 



ZZ2T 



In four-part harmony a mixture of these three kinds of motion often occurs, 
for example, in Ex. 6, at b, the soprano and tenor move in similar motion, 
while contrary motion is found between soprano and bass, or tenor and bass, and 
oblique motion between alto and all the other voices. 

The already-mentioned faulty progression of consecutive fifths or octaves can 
only occur in similar motion, when any two parts, distant from each other a 
perfect fifth or octave, proceed simultaneously to such positions in the ensuing 
chord that they are still separated by the same interval. 



10. 



P 



Octaves. 



"ST - 



n.p 



Fifths. 



rr?' 



THE RELATION OF ONE VOICE TO ANOTHER. 



18 



The following example contains both faults : — 

6. 



12. 



7 


7 -^-^ — 1 


1 


— g» -^ ^ 


BE 


g ' w ■ 


1=g ^ s 


— » » « — 


tr 




-&- / <^> 






(= > /"-J 1 


iTJ ^' ^ 


<•). 








V rj ' 













The forbidden parallels are here indicated by the oblique lines. In example 
a there are consecutive octaves between the soprano and bass, and consecutive 
fifths between the alto and bass ; consecutive fifths are also found in example b } 
between tenor and bass, and in example c, between soprano and bass, and soprano 
and tenor ; and octaves are found between alto and bass in example b, and 
between tenor and bass in example c. 

The best means of avoiding such faults as the foregoing is to employ, in all Consecutive 
cases where they are likely to occur, contrary motion between the three upper octaves— how 
voices and the bass, or (if there be a convenient note in the ensuing chord) the av01 
oblique motion. Thus, in the following example, at a, the bass moves in oblique 
motion with the soprano, and at b and c in contrary motion with all the upper 
parts : — 

6. c 



13. 



P 



ZZ2Z 



E5£ 



S 



S 



~W 



=£ 



IZ2I 



77" 



321 



The musical ear will readily perceive that the foregoing rules are not dictated Why pro- 
by caprice, although it is difficult to give any reason for the interdiction of conse- 
cutive fifths. The prohibition of the octaves is, however, more intelligible, and 
has its foundation in the fact that the doubling of a note, although it adds one 
voice to the harmony, does not add any new interval to the chord, and therefore 
if the same voice be doubled in two successive chords the effect of a four-part 
phrase is lost as far as regards the harmony. 




±E 



3E 



~tzr 



In Ex. 14 the tenor forms consecutive octaves with the soprano, and is 
on this account useless, as the phrase contains precisely the same harmonies as 
Ex. 15, which is written in three parts. 



14 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



Hidden fifths 
and octaves. 



Exercise for 
the employ- 
ment of the 
common 
chords. 



^ 



Another, though less grave fault occurs when the second interval formed by 
two voices moving in similar motion is a perfect fifth or octave, thus : — : 



16 'P 



2Z 



zzz 



zr: 



...C3_ 



Z^Z 



rs: 



^r 



Such progressions are termed hidden or covered fifths and octaves. They will 
be more particularly described hereafter, as there are cases in which they are 
allowable and even advisable. For the present, however, the exercises will, if 
correctly conceived, offer little or no opportunity for making objectionable hidden 
fifths or octaves. 

Our next exercise will be to employ the three principal common chords in 
connection with each other, musically and with strict observance of all the 
foregoing rules. For this purpose we will employ the following (or any similar) 
bass. 

Exercises. 





1. 












2. 










-IF7 W^f\' 








— & — 








— e> — 




C-^ 


H 


17. *&* f 


fj 




f-J 






r^ 


i*"j 




rj 




r -> ii 
























"* H 


C 
3. 

7^1 


: I. 


V 


I. 


rv. 


V. 


I. 




rj 








&^~ 






f-> 




r -t 








rj 




■ /~D 



























N.B. — These as well as all following exercises are to be continued as long as it is 
deemed necessary. The exercises given in this boot are merely intended as indications of 
the manner in which the practical studies are to be pursued. 

The Roman numerals under the examples signify the degrees of the scale on 
which the roots of the various chords are situated (see p. 10). They are always 
to be added by the pupil in all succeeding exercises. The letter followed by a 
colon, thus, C : indicates that the phrase is in the key of 0. (N.B. — It is 
absolutely necessary for the plan of this work that these signs should be under- 
stood and adhered to from the beginning). 



CLOSE AND EXTENDED HAEMONY. 

Cl ose A chord is said to be in close harmony when the three upper parts are as close 

harmony. to one ano ther as possible, i. e. within the compass of an octave, the bass being 

more or less distant : — 

a. b. c. 

m 



18. 



¥ 



~g7~ 



Sz 



nz 



:ez: 



CLOSE AND EXTENDED HARMONY. 



15 



In the above example the same chord is shown in different positions, but always 
in close harmony, there being no room to double or invert any one of the 
intervals in the octave, without overstepping the boundaries of soprano and tenor. 
If, for example, the tenor of the chord a be inverted in the octave, it will pass the 
soprano, and the chord will be altered as at b. If, on the other hand, the soprano 
be inverted in the octave, the chord will appear as at c. 

By extended harmony is meant an arrangement of a chord in which the Extended 
soprano and tenor are separated by a greater distance than an octave, and in harmony, 
which there is room for the soprano and tenor to be inverted in the octave 
without encroaching on each other. 



i 



-7rr 



c. 



3E 



19. 



ZZ3Z 



32= 



=S2= 



In the first three bars of the above example the chord is shown in extended 
harmony. If in chords a and b, the tenor be inverted in the octave, the soprano 
will not be reached, and the chords will appear as at d and e. If the soprano of 
the chord c be inverted, the tenor will not be encroached upon, and the result of 
the inversion will be the chord /. 

These two kinds of harmony seldom appear alone, a combination of both 
being generally employed. For the present, however, as the extended harmony 
presents more difficulties than the close, we will make use exclusively of the 
latter. 

The position of the first chord of a harmonic phrase is decided by inclination, 
that of the succeeding chords is then regulated by it. Nevertheless, for the sake 
of facilitating the working of the exercises, the best position of the first chord 
will for the present be indicated as follows : — If the first bass-note be figured 
with a 5, it is intended that the fifth of the chord should be given to the soprano ; 
a figure 3 over the bass-note shows that the chord requires the third to be placed 
at the top; and if there be no figure whatever over the bass, the octave should be 
placed at the top of the chord. This arrangement need not necessarily be adhered 
to, as almost any example in close harmony might be written in three different 
positions. The position irfdicated by the figure of the first bass-note will however 
be found best adapted to form good progressions, at least until the pupil has 
gained experience, 

The correct working of Ex. 1, No. 17, will therefore be as follows: — 



The two kinds 
generally used 
in combina- 
tion. 



The position 
of the first 
chord indi- 
cated in the 
examples. 



16 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



20, 



\2 „ j 






.... .j. _| _ 




m — S^ 


-\£3f~ 




— ^M — g*= 




xJ. » 




-S 


« i ^ 




(jr <-* c*t — c* ^ 




CJ 






rj 




if ;. 












\. — i-j 




rj 






/"J 















C: 



V. 



IV. 



V. 



Authentic 
cadence. 



Plagal 
cadence. 



The natural relationship of these chords one to another wall readily be seen 
by observing the connections. (N.B. — These connections should always be 
indicated by the pupil by means of the slur ""■■"', as in the above example). 

From the feeling of rest and satisfaction induced by the concluding progres- 
sion iu the above example (that of V-I), it has been named the perfect close, or 
authentic cadence. It is formed, as will be seen, by the chord of tonic, preceded 
by that of the dominant. Another kind of cadence or close, called the plagal 
cadence, is formed by the chord of the tonic, preceded by that of the subdominant. 
(N.B. — The last chord of a cadence always falls on the accented part of the bar.) 



21. 



\ 



Authentic Cadence. 



ez: 



V. 



-jCZL 



22. 



;z2: 




w 



Plagal Cadence. 
9: 



IV. 



re2i 



-§= 



I. 



These and other cadences will be more fully considered in a later chapter. 

In order to become well acquainted with the peculiar progression between the 
fourth and fifth chords in example 20, it would be advisable to write out several 
similar progressions of IV-V and V-IV in various keys and in close and 
extended harmony. 



Secondary 
common 
chords of the 
major scale. 



OF THE OTHEE COMMON CHOEDS OF THE MAJOE SCALE. 

The common chords situated on the other degrees of the major scale, although 
they certainly belong to that scale, yet are not so closely related to it as those 
already mentioned. 

To distinguish them from the three principal chords, we will call them 
secondary common chords. They are found on the second, third, sixth, and 
seventh degrees of the scale. 



23 



P 



SE 



n. 



SEE^S 



m. 



OF THE OTHER COMMON CHORDS OF THE MAJOR SCALE. 



17 



The chords on the second, third, and sixth degree are minor chords, being 
composed of a minor third and perfect fifth. 

In order to distinguish between major and minor chords in the system of 
Roman numerals under the bass-notes, we will employ a large figure for tbe 
former and a small one for the latter. The beginner must beware of mistaking 
any of these chords for chords of the tonic. As long as the key remains major, 
as in the above example, the various chords of F, G, &c, are merely chords of 
the different degrees of C major, and cannot belong to the key of F or G, unless 
such keys are called forth and substantiated by modulation. 

Hence it will be easily seen that each chord may have several significations, Chords belong 
i. e., it may belong at once to several different keys. different 

Thus, in the following example, scales. 



24. 



C: I. F: V. G: 



-s^- 
IV. 



the major chord of is shown as belonging to three different keys, those of 0, 
F, and G. 

In the first of these keys it appears as tonic chord, in the second as dominant, 
and in the third as subdominant. 

No new rules are required for the connection of the secondary chords with 
each other, or with the three principal chords. The following remarks may 
however not be inappropriate : — 

The progression of the three upper parts will always depend on that of the Progression of 
bass. This latter may be of two kinds, viz., firstly, by leaps of at least a third, 
in which case a connecting link between two chords will always be found in some 
note which belongs to both, and which will then be allowed to remain in the same 
voice, according to the rule given at p. 11 ; and secondly by degrees, when it will 
generally be advisable to employ contrary motion between the bass and the upper 
parts as already explained at p. 13. 



the bass. 



25. 



llm 



Better so. 
c. 



g 



E££ 



ES 



!Sd 



-<s>- 



H=S^E 



E5£ 



m 



7Z2Z 



TV. 



V. 



In the above example the bass proceeds by leaps of various distances, the 
upper parts being connected by notes which belong to both chords and which 



18 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



remain in the same voice. A strict adherence to this form of progression 
between the chords of the second and fifth degrees, shown as b, in the above ex- 
ample, occasions hidden octaves between the bass and tenor, which are better 
Objectionable avoided by means of the progression given at c. The reason why such hidden 
octaves are objectionable is that the upper voice proceeds a ivhole tone, and their 
effect would be still more unpleasant if they occurred between the extreme 
voices, thus : — 

b. 



hidden 
octaves, 



Allowable 

hidden 

octaves. 



26. 



a. 

-&- 



_£2_ 



£ 



P- 



The progression may be improved by employing contrary motion between 
the extreme parts as at b. 

Hidden octaves cease to have any unpleasant effect when the upper voice 
proceeds only a semitone, thus : — 



27 



P 



rcrr. 



ZZ21 



m 



rszn 



When the bass proceeds diatonically, contrary motion will always be em- 
ployed ; in one position, however, shown in the following example at a, it will be 
advisable to double the third in the second chord in order to avoid the hidden 
fifths which would otherwise occur between soprano and tenor 



28. 



Better so. 



Jft^s^ 


m^f- 




-fcSr 




—fS-A 


-c&&- 




n 


— & — 


— & — 


















Z2~ 








IT" 














<"P 










^-- rj 




(*■--> 




fj 







































C: I. 



m. V. IV. 



I. 



Hidden fifths. Hidden fifths such as occur at a in the above example are still more percep- 
tible when the chord appears in an extended position. 



29. 



=#= 


a. 




r?_ 


-- n 


b. 




rr> 


£j= 


£ 




■— r? 


— e — 


■ — rj 




— s— 


— <s> — 






-* CJ " 


-<=2- -G3- 






J2. 


"g- 


»* 




i — ■ 1 


1 VJ 




r^i 




r^/ 




hH 


1=1 




rz> 


s 







OF THE OTHER COMMON CHORDS OF THE MAJOR SCALE. 



19 



The progression b is preferable. If however the hidden fifths are between Allowable 



the middle voices, they are less objectionable. 



hidden fifths. 



30. 



I 



S 



L 
8L§1 



■rlr 



p 



?= 



EXEKCISES. 
2. 



-(= 



-m- 



-f=> 



■JPC^L 



C=£ 1 



3. 



^ 



4. 



5. 



S 



e 



& 



122 



1" 



ez 2=2 



=g 



& 



g 



P3 



a 



a 



^ 



zz 



The fourth of the above exercises will require some little explanation. It Sequence, 
will be observed that the progression of the bass in the first bar is repeated in 
the three succeeding bars. Any such regular progression is termed a sequence, 
and demands a like regularity in the progression of the accompanying voices. 
This regularity could not be obtained by working exactly according to the rules 
already given, thus : — 



zzs£zz 



32. 



etc. 



2=£ 



:<=z: 



^ 



=^= 



It will therefore be necessary to make a leap at the end of the first bar, in 
order to bring the first chord of each bar into the same position, and thus preserve 
the uniformity of the sequence. 

-J— 



33. 



P 



sk 



i£ 



etc. 



m 



^ 



^= 



-f=_ 



=£2- 



A similar sequence is also contained in the first exercise of Ex. 31. It is, 
however, one which can be accompanied without any deviation from rule. 

In the third bar of the fourth exercise we find a chord which we have not yet chord of 
considered, but which differs in many important respects from all other chords, g^^ 8 
This is the chord on the seventh degree. Upon examining it we find that it is 
composed of a minor third, and a fifth which is smaller by one semitone than the 



20 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



perfect fifth. On this account the fifth is termed diminished, and the chord itself 
has received the name of the diminished common chord, or chord of the diminished 
fifth. 

The interval of a diminished fifth may he formed from any perfect fifth by 
chromatically raising the root, thus : — 

Perfect 5th. Diminished 5th. 



Inversion of 
the dimin- 
ished fifth. 



Require 
resolution. 



Resolution of 
diminished 
& augmented 
intervals. 



Resolution of 
the leading 
note. 



34 -i 



¥ 



Since the diminished fifth is smaller by one semitone than the perfect fifth, it 
follows that its inversion will be one semitone larger than the perfect fourth. 
This inversion is therefore termed the augmented fourth. 

Perfect 4th. Augmented 4th. 



35. 



P 



zr 



Both augmented and diminished intervals are dissonances, and as such 
invariably require to be followed by some other harmony in order to render them 
inteUigible. 

The progression of any dissonance into the following harmony is called its 
resolution. 

It may be accepted as a rule, that the natural resolution of any note forming 
a dhninished interval is diatonically downwards, while that of an augmented 
interval is upwards. 

This rule is observed in the resolution of the chord of diminished fifth on the 
seventh degree of the scale, but in addition to this, the progression of the root of 
this chord will require consideration. The seventh degree of the scale (which is 
the root of the chord in question) has always a strong tendency upward, towards 
the tonic or first degree. On this account it is called the leading note. 

This upward tendency will be readily perceived in the following example : 



36, 



"s>~ 



V. L 

which is more satisfactory in its effect than — 



37 






Or, 



V. 



vx 



P 



■"E7 - 



~!rr 



^- 



OF THE OTHER COMMON CHORDS OF THE MAJOR SCALE. 



2.1 



In accordance, then, with the upward tendency of the leading note, and Resolution oi 

observing at the same time the rule for the progression of diminished intervals, diminished 

the natural resolution of the diminished fifth on the seventh degree will be as fiftiL 
follows : — 



38. 



I 



Inversion. 



9 



:2: 



ZJC2Z 



~a~ 



The chord of diminished fifth will therefore resolve itself into the chord 
of the first degree, hut in an incomplete form, i. e. without the fifth ; thus: — 



39. 



I 



V 



zasz: 



In the system of Roman numerals a small o is added to the number, to denote that the 
chord is diminished — thus viio. The correct figuring of all the chords of the major scale 
will therefore be as follows ; — 




The resolution of the two notes forming the interval of the diminished fifth Doubling of 
being thus determined by rule, it is clear that if either of these notes be doubled intervals of 
both the note and its duplicate must have the same resolution, the result of which ^imfnU haH 01 
would be consecutive octaves. ^h. 



41. 



W 



ig=sj 



Or, 



£h 



IC2I 



{In 



-s- 



On this account it is forbidden to double either the root or the fifth of this 
chord; if, therefore, it is used in four parts it will be necessary to double the third, 
which is then made both to ascend and descend. 



42. 



J 

I 



P 



=B= 



S 



OF THE COMMON CHORDS OF THE MAJOR SCALE. 



Free progres- 
sion of the 
leading note. 



Extended 
form of the 
authentic 
cadence. 



The progression of the third of the chord of diminished fifth is not always 
limited to a single degree ; under certain circumstances it may also descend 
by a leap into the fifth of the ensuing chord. 



43. 



:22T 



^ 



Or, 



I 

1 



P 



w 



In the third bar of Ex. 33 we have already found an exception to the above 
rules, both as regards the doubling and progression of the leading note. The 
exception has its excuse in the necessity for preserving a regular progression of 
the sequence. 

The already-mentioned authentic cadence (p. 16) is seen still more distinctly 
in the preceding exercises. For, while the natural relationship of the chord of 
dominant to that of the tonic makes these two chords the most suitable for the 
formation of a cadence, in the first and second exercises of Ex. 31 may be 
observed a preparation of the cadence by means of the chord of the second 
degree, which bears the same relationship to the chord of dominant as this latter 
does to that of the tonic. 



44. 



=t 



~cr 



3 



± 



~cr 



3=z: 



122" 



n. 



V. 



V. 



In addition to the chord of the second degree, the chord of subdominant may 
also serve to prepare the authentic cadence. 



45. 






H=2- 



IV. V. 



23 



CHAPTEE II. 



OF THE COMMON CHOEDS OF THE MINOR SCALE. 



The three principal chords of the major scale were found on the first, fourth, 
and fifth degrees. Those of the minor scale occupy the same positions. 

The peculiarly final feeling induced hy the authentic cadence is caused by 
the fact that the last chord hut one contains the seventh degree of the scale, 
or leading note. According to the signature of the minor scale, however, the 
seventh degree is distant a whole tone from the tonic, and therefore does not 
possess the characteristics of the leading note. 

In order, therefore, to make the authentic cadence m a minor key, it is 
necessary to raise the seventh degree chromatically one semitone, by which means 
it becomes the leading note of the scale. 



The principal 
chords of the 
minor scale. 



Alteration of 
the seventh 
degree of the 
minor scale. 



P 

46. 



~?g~ 



zzz: 



P 



zzsz 



In consequence of this alteration the chord of the dominant is precisely the 
same in major or minor (i. e. it is always a major chord). 

A Minor. _ n * A Major. 



47. 




Dominant 
chord of the 
major and 
minor scales 
identical. 



Observe that just as the major or minor chords are expressed by large or small Eoman 
numerals, so are major or minor keys expressed by large or small letters. Thus a : signifies 
A. minor, A: A major. 

As a proof, however, that a similar alteration of the sixth degree is not 

allowable, it is only necessary to examine the plagal cadence, shown at a in the 

following example, which, it will readily be seen, could not possibly be formed 

as at b. 

a. b. 



Alteration 
of the sixth 
degree not 
possible. 



48. 



# 



E^£ 



Sr 



^ 



24 



OF THE COMMON CHORDS OF THE MINOR SCALE. 



The minor scale in its correct harmonic form, in which it serves as the 
groundwork for all the harmonies of a minor key, is therefore as follows : — 



49. 



m-. 



=8=2 



All other forms of the minor scale, such as 
— CT „ 9*-**^ 



P 



have their origin in rules relating to melody, which rules will he duly considered hereafter. 
It may, however, be here observed that their object is to avoid the progression of an 
augmented second, i. e., a second which is larger by one semitone than the major second 
(such as occurs between the sixth and seventh degrees of Ex. 49), which interval, on account 
of its harshness, and the difficulty of intonation it presents to the singer, ought seldom, if 
ever, to be introduced. 

The three principal chords of the minor scale may be thus represented in 
*heir relation to each other : — 



50. Ml 



Secondary 
chords of the 
minor scale. 



OF THE SECONDARY CHORDS OF THE MINOR SCALE. 

According to the above explanation of the minor scale the secondary chords 
will appear as follows : — 



P 



51. 



-#- 



S=gE 



HI'. 



VI. 



Augmented 

common 

chord. 



The second degree bears the same chord of diminished fifth, which has 
already been found on the seventh degree of the relative major scale. A similar 
chord is also found on the seventh degree. 

The chord on the sixth degree is major, and the third degree bears a common 
chord which has not yet been met with. This chord consists of a major third, 
and a fifth which is larger by one semitone than the perfect fifth, and on this 
account is called an augmented fifth, and the chord itself is known as the 



OF THE SECONDARY CHORDS OF THE MINOR SCALE. 



25 



augmented common chord, or chord of the augmented fifth. (In the system of 
Roman numerals an augmented interval is expressed by a dash, thus '; the chord 
in question would therefore he figured III'). 

The peculiar nature of this chord renders its combination with other harmo- its combina- 
aies very difficult. It is on this account very seldom used. other"chords. 




m 



^3(9- 






fgES3|iE:]^3EfctiE: 



zj: 



-tzt 
6 



ZZ2T 



jczrri 



VI. 



i. hi'. n°. n°. nr. iv. rv. nr. 



v. nr. vi. vi. nr. n°. 



Of the above progressions, the most serviceable are those at c and d, the 
preparation (i. e. the progression from the preceding chord) being least harsh at 
d, where the note which forms the interval of an augmented fifth {viz., the G $) 
appears as a consonance in the preceding chord. 

The augmented common chord which appears so often in modern music is 
however not the one just mentioned, but belongs to the class of chromatically 
altered harmonies, and will be explained hereafter in the chapter on Altered 
Chords. 

The rules relating to progression, &c, are all to be observed in the exercises Progression 
on the chords of the minor scale. Here, too, will be seen the full application of u^m^ted 
the remarks which were made on the upward tendency of the leading note, since se c° ud - 
if the leading note of the minor scale were to descend to the sixth degree, the 
result would be the anti-melodic progression of the augmented second, which 
interval, as has already been observed, is better avoided (at least when the two 
notes of which it is composed belong to two different harmonies). 



53. 



P 



bte 



m 



V. 



"%r 



ES 



Ssc 



VI. 



VI. 



In order, then, to form the connection between the chords of the fifth and Progression 

sixth degrees, it will be advisable to allow the leading note to ascend, which will chord of the 

have the effect of doubling the third in the chord of the sixth degree. tottift afWw 

B sixth. 



26 



54. 



1 
I 



OF THE COMMON CHORDS OF THE MINOR SCALE. 



-e-+3E 



^33 



SSs: 



12222: 



S 



:2222I 



etc. 



~27~ 



a: V. VI. V. VI. 



VI. VI. 



V. 



VI. 



The only means of correcting Ex. 53 b (if it were necessary to have the first 
chord in the position there given), would be to introduce a note in the soprano 
between the two chords, thus : — 



m 



a: VI. 






i. 



*• 



56 



.&£ 



& 



5=M 



Exercises. 



2. « 



^db=dH 



?Z^ 



j=t 



rp 



zz 



3. 



# B# 



^ 



Sf2 



*= 



=2 



:^ 



4. 8 # 

3: 



±P= 



z=£ 



;<==" 



1 



a 



g 



6. 6« 



o 



P2- 



rs 



Methods of 
figuring 
various 
chords. 



REMARKS ON THE ABOVE EXERCISES. 

A chromatic sign ($, \j, or j|) over a bass note without any figure (as in the 
third bar of exercise No. 1) has reference always to the third of the chord. The 
common chord is seldom figured at all ; those bass notes, therefore, which bear 
no figure are always accompanied by a common chord. Sometimes, however, it 
is necessary to figure the common chord — this is done by means of the figures 3, 

Q 

5, 8, \ or 5. In the third and sixth exercises it was necessary to indicate the 

3 
common chord by means of a 5. Here the augmented common chord has been 



COMMON CHORDS OF THE MAJOR AND MINOR SCALES. 



27 



introduced, and the sign 5 $ being placed over the bass note signifies that the 
fifth is sharpened. If the sharp had been placed alone, it would have affected the 
third of the chord. A figure 3 or 5 is also sometimes used to denote the position 
of the first chord of an exercise. (See p. 15.) 

If the rules relating to the progression of parts be strictly observed in accom- 
panying exercise No. 1, the anti-melodic progression of an augmented second 
will occur in the alto in the third bar. 



Progression 
of the 
augmented 
second. 



57. 



m 



p=i- 



:?5 



=^= 



=9= 



SE 



=& 



^ 



=^t 



^2= 



T2~ 



To avoid this, it will be necessary to deviate slightly from rule, and to How avoided 
allow the alto to descend from / to e, the soprano and tenor also decending 
to those notes of the succeeding chord which He nearest to them, namely 
g | and b. 



58. 



P 



m 



^ 



=S- 



^ 



ZZ2Z 



=P= 



It would also be possible to keep the connection of the b in the soprano, by 
giving to the tenor a leap downwards from d to g§. In this case the close 
position will be abandoned, and the two last chords will appear in extended 
harmony. 



59. 



\ 



=s : 



^ 



=sfe 



H 



~T2- 



Before proceeding to the farther employment of the common chord, we will 
form a table of all those chords with which we are as yet acquainted. 



( 28 ) 



COMMON CHORDS OF THE MAJOR AND MINOR SCALES. 

Major Scale. 



1 



¥ 






60. 



C: I. u. m. IV. V. 

Minor Scale. 



£ 



¥ 



a: i. 



ii". 



nr. iv. 



Major chords are found- 



In Major. 



In Minor. 



1 



9 



^=s = 



0: I. IV. V. a:V. VI. 

Minor chords are found — 

In Major. In Minor. 



I 



C : n. ni. vi. 



rv. 



Diminished chords are found- 
In Major. In Minor. 



w 



C : yd". 

An augmented chord is found — 



~-§r - v1? 



P 



In Minor. 



-fftS- 



a: HI'. 



vi. vn" 



Ej g ^ — p—l 



VI. vu°. 



( 29 ) 



CHAPTER III. 

OF THE INVERSIONS OF THE COMMON CHORDS. 

The employment of the common chords is not confined to the positions shown Inversions of 
in the foregoing examples, where the root alone is used as hass. The third or chord. 
fifth of the original chord may also serve as bass, and thus new chords will be 
formed, derived from the common chords, and termed inversions. 
Two inversions of the common chord are possible — 

(1). When the third of the chord is employed as bass. The chord thus Chord of 6. 
formed is called the chord of the sixth. 



61. 



i 



Chord of the sixth, 
- . . , ,,. , situated on the third of the 
Original Chord. root. 



v 



ZZ2Z 



(2). When the fifth of the chord is employed as bass. The chord chord of ?■ 
formed by this means is called the chord of the sixth and fourth. 



62 



P 



_ , . Chord of the sixth, and fourth, 

Original Chord. placed on the ftfth of the root. 



ES 



These two chords are distinguished by means of the signatures 6 (or some- 
times 3 ) and 4 placed over the bass thus : — ■ 



63. 



m 



~J?ZL 



Observe that the Roman numerals continue to indicate the degree of the 
scale on which the root of a chord is situated, and do not refer to the position of 
the bass. Thus, in Ex. 63, the three chords are all figured I., although the 
bass of each is on a different degree of the scale ; because they are all derived 
from one and the same root, namely, C. 

Similar inversions may be derived from all common chords. 

By means of the employment of the inversions of chords, the harmonic pro- 
gression obtains greater variety, and the progression of individual parts, and 



30 



OF THE INVERSIONS OF THE COMMON CHORDS. 



Doubling of 
one of the 
intervals of 
the chord of 
sixth. 



especially of the bass, becomes more flowing. According to the rules relating to 
the doubling of one interval of the common chord, (see p. 11) the root of the 
original chord, that is, the sixth in the chord of sixth, -will be best doubled when 
the chord of sixth is used in four parts. The bass of the chord of sixth must 
only be doubled when the natural progression of parts renders it necessary, or 
when by so doing certain faults may be avoided. The leading note should never 
be doubled, whether it appears as third in the chord of dominant, or as bass of 
the chord of sixth. 



64. 



i 



Good. 



¥ 



m 



~&r 



_r2_ 



s 



65. 



Bad. 



-? 




T— 5— 


«J 


/l - 








-^ 


W 


(n\ 






1 






v/ 






J 






J \& ■»- 


e 


fiV 










(W. 










v — 


rj 








■& — l 






b^- 1 





The position of the three upper parts of either of the inversions is determined 
by the natural progression of parts, and has no influence on the chord itself. 
The chord of sixth is therefore to be met with in the following forms : — 



66. 



P 



i: 



C: I. 



2Z 



rs 



-j^r 



-rj- 



ESE 



etc. 



32= 



Employment 
of the chord 
of«. 



The chord of sixth and fourth occurs less frequently than the chord of sixth, 
and depends on certain conditions which will be explained hereafter. It is most 
frequently met with in the formation of cadences (closes). The bass note (the 
fifth of the original chord) is most suitable for doubling, and the chord will be 
found in the following and similar forms : — 



67. 



w 



I 



SE 



BE 



C: I. 



2Z 



321 



zrzi 



etc. 



No new mechanical rules are required for the connection of these chords 
■vrith the others; we therefore now proceed to show the application of the inver- 
sions or derived chords in the following exercises. 



REMARKS ON THE PRECEDING EXERCISES. 
Exercises. 



31 



6 
43 



2 



I 



88. 



zi 



5=z 



i=^= 



22: 



zz 



^= 



:=2=z5t 



E 



3. 



s 



B FEP?3f¥ 



7rJ- 



22: 



=sfc 



22=: 



=pz 



22: 



2= 



t=3 



s 



6 
4 3 



2= 



6 
4 3 



221 



=& 



22: 



22: 



S 



22==^ 



5. 



jjJE 



6 6 6 6 



I& 



22. 



¥■ 



F=^ 



6 6 6 6 



221 



22: 



S: 



22: 



t4± 



^ 



■22= 



F 



7. 



S 



3 6 6 



6 
4 3 



6, 6 



7=2=^ 



«t 



I 



22- 



?= 



^ 



22 



E± 



zi 



^ 



t=t 



rf-g-F 



§§E 



=& 



i 



8 # 



10. 



^ 



^ 



22; 



E=f 



22: 



P 



22: 



m 



6 

4 tt 



11. 



6 



=^ 



221 



22= 



*=£ 



22: 



REMARKS ON THE PRECEDING EXERCISES. 

/n the first bar of Ex. 2, the position of the chord is indicated by the figure 
5 being placed over the bass. The chord is therefore to be written with the fifth 
in the soprano or upper voice. A similar system is observed in all following 
exercises. If there is no figure over the bass note, it is understood that the octave 
shall be given to the soprano. 

In the second example the chord of diminished fifth appears in its inverted Inversion of 
form as chord of the sixth. It is most used in this form. Its resolution always S^Xed '* 
depends on the progression of the bass, which in most cases is as follows : — fifth - 





6, 




6 


6 


r»v 




69. (££- 


— S 1 


— r2 


p 


3 _ 








i 





32 



OF THE INVERSIONS OF THE COMMON CllOKij..*,. 



Free resolu- 
tion of the 
augmented 
fourth. 



The upper parts may then proceed thus : 



70. 




fesfe 



tozgi 



d= 



Z2t 



=b i d .J ii J Je 



3=t: 



J 



itzz=t 



-23- 



(£1 



-' ^ JT^- 



2=£ 



^ 



^ 



-£2= 



-P2= 



-t 



=^ 



=Z2= 



:t 



From the above example it will be seen that the inversion of the diminished 
fifth, i. e., the augmented fourth, does not require so strict a resolution in four 
parts as was given at p, 21, Ex. 38, for the same interval in two parts. Thus in 
the first bar we see the fourth f-b in soprano and alto proceed in similar motion 
to the fourth g-c. As this chord produces a somewhat similar effect on the ear to 
the chord of dominant seventh (which will be mentioned hereafter) beginners 
often feel constrained to resolve the diminished fifth strictly, even when it has 
become changed by inversion into the augmented fourth. This is, however, only 
necessary when it appears in its original form as a real diminished fifth. Such a 
progression as the following is therefore objectionable on account of the consecu- 
tive fifths. 



Allowable 
consecutive 

fifths. 



71. 



I 



V 



IZ21 



S 



It may here be observed that consecutive fifths, when one is perfect and the 
other diminished, are allowable, provided always that the diminished fifth shall 
follow the perfect, and not vice versa. Thus, the following examples are good : — 



72. 



P 



:za: 



:c2: 





6 


e 


6 


4 
8 


7mT'~~ 




\Fh 


n 


1-=3> 


""■■J 









Various other 
resolutions of 
the dimin- 
ished fifth. 



The progression of the parts of a chord of diminished fifth (or its inversion) is 
however otherwise, when the bass does not proceed to the chord of the tonic. For 
example : — 



73. 



22: 






: s : 



a— <=*=r 



:c2: 



=8= 



^ 



^ 



E^ 



etc. 



-• 



IV. 



vn" 



VI. 



REMARKS ON THE PRECEDING EXAMPLES. 



S3 



The chord of diminished fifth found on the second degree of the minor 
scale is capable of yet other resolutions, as in this chord the root may be 
doubled. For example : — 



74. 



:a_ 



m 



3: 



~^r 



11° 



fe 



Eg: 



The succession of two or more chords of the sixth on a bass which Sequence oi 
proceeds diatonically (as is shown in Ex. 68, No. 3) requires that one or ° or s 
more of the upper parts shall move in contrary motion with the bass. For 
example : — 



75. 




The sequence of chords of the sixth in Nos. 5 and 6 of Ex. 68 is best accom- 
panied, when the regular progression of the bass is observed in all the other 
parts, thus : — 



76. 



9 



i 



S3 



-nr 



-^Imlrnk 



~^r. 



^ 



■&z 



etc. 



Covered octaves, such as occur between tenor and bass in the second and 
third bars, cannot in such cases be avoided. In fact exceptional progressions like 
the above must sometimes be permitted, when to have adhered strictly to rule 
would be to mar the unity of the phrase ; experience alone will decide where 
such exceptions are allowable. 

In Ex. 68 we find the cadence (already mentioned at p. 16) rendered clearer Anthentio 

and more decided by the chord of 4 ; it may then be accepted as a rule that the Spared by 

second inversion of the chord of the tonic, (i. e. the chord of 4 ,) when followed the chord 

of 5 



54 



OF THE INVERSIONS OF THE COMMON CHORDS. 



by the chord of the dominant, has a strong tendency towards an authentic cadence 
or close. 



77." 



m 



W=Fz 



^= 



The chord of | is often preceded by the chord on the fourth or second 
degree. 



78. 



6 

4 



i 



=s= 



&& 



m 



C: IV. 



fr 



=& 



s 



^= 



V. 



Although the chord of 4 is very effective in the above position, and also in 
modulations into foreign keys, yet under other circumstances it is extremely weak, 
and its employment is therefore subject to certain conditions, which will be treated 
of later. 



A line through a figure thus, B, as seen in Ex. 68, Nos. 8, 9, 10, indicates that the interval 
is to be raised chromatically one semitone. Sometimes a J or j^ is used to express the same 
chromatic alteration. 



( 35 ) 



CHAPTER IV. 



OF THE CHORD OF THE SEVENTH. 



The chord of the seventh is founded on the common chord, and is formed by Construction 

of the chord 
the addition of a new third to those of which the latter is already composed. The of 7. 

new interval forms a seventh from the root. 



79. 



M 



7 



The new chord is not so independent as most of the common chords, but has Its charac- 
a distinct tendency towards a resolution. On this account it can never appear 
except in conjunction with other harmonies. It serves to render the relationship 
of one chord to another closer and more intimate, and its employment therefore 
offers considerable advantages with respect to harmonic connections. 



THE CHORD OF THE DOMINANT SEVENTH IN MAJOR AND MINOR. 

Of all the chords of the seventh, the most important is that found on the fifth The chord of 
degree of the scale ; it is formed of precisely the same intervals in major as in nant 7. 
minor, viz., of the major common chord with the addition of a minor seventh. 



80, 



I 



± 



mw^EM= 



0: V. 



In figured bass it is indicated by a 7 over the bass note, and in our present 
system of Roman numerals by V7. 



81. 



<e u n 



C: 



V, 



G: V, 



36 



OF THE CHORD OF THE SEVENTH. 



The relation which the chord of the dominant bears to that of the tonic has 
been already demonstrated by means of the cadence ; it will however be rendered 
still clearer by the use of the dominant seventh. 



82. 



F# 




rj 







w- 


7 


^-^ 


LfeJ 

7 
» 





a: V, 



Observe that the chord of tonic which follows that of dominant seventh is incomplete ; 
in both cases the fifth is omitted, the reason of this will be perceived from the following 
paragraph. 

Its resolution. The marked tendency towards a resting-place or close exhibited by this 
chord and the consequent connection of it with a common chord, is called 
the 

RESOLUTION OF THE CHORD OF SEVENTH. 



If the chord is resolved into the chord of the tonic as in Ex. 82, it is also 
called the perfect close (authentic cadence). For the present we shall consider 
this as the natural resolution of the chord of the dominant seventh. 

The resolution takes place as follows : — 

The progression of the bass being given, a resolution upwards of the seventh 
will be found impossible, while its descent will be in every respect satisfactory to 
the ear. 



83 



P 



EB 



resolution The third of the chord of dominant seventh is always the leading note of the 

inthecuordof scale; its natural tendency is therefore upward : thus in the following example a 
dominant 7. j s more satisfactory in its effect than b. 



84. 



a. 

i — H 1 




b. 




■# 3 


rj 1 -r> ~ 





m — : H — 


— S ■" 


=- & 




1 ^ 1 


7 _ 


1 ,g u 



RESOLUTION OF THE CHORD OF THE SEVENTH. 



37 



The latter progression is however less unpleasant when the third appears in a 
middle part. 

b. 
: r j 



85, 






7 



zaz 



The downward resolution of the third is therefore allowable under the following Downward 

,... progression of 

conditions :— the third. 

1st. When it is in a middle part, and not at the top of the chord ; and 
2nd. WheD the bass moves in contrary motion with it. 



86. 









Bad. 




U — , 








/L ^ 


rj 


g. 


rj 


In <-> -~~ 








\J rj 




rj 


S 


xJ 


7 




7 




iVr 




r-j 




(P). 








^ — 


-. rj 




~"" --j 


s> — => 









The reason of the last rule is that if the two parts move in similar motion 
hidden fifths will occur. 

The progression of the fifth of the chord of dominant seventh is free. It Progression of 
generally descends with the seventh ; the progression of parts may however require e 
it to ascend as in Ex. 85 at b, where the d in the soprano proceeds to e in the next 
chord. 

The following then are the rules for the ordinary resolution of the dominant Resolution of 

,! the chord of 

seventh : — dominant 7. 

The seventh descends one diatonic degree. 

The root proceeds a fourth upward or a fifth downward. 

The third ascends one degree. 

The fifth can either ascend or descend one degree. 

The relationship of the third and seventh to one another recalls what has already been said 
(p. 21) on the resolution of the diminished fifth, this interval being again found and similarly- 
resolved in the chord of the dominant seventh. 

87. 



The chord of dominant seventh in its present form seldom occurs in the Its employ- 
middle of a composition, and when so employed the feeling of a perfect close men ' 
should be avoided. 



38 



OF THE CHORD OF THE SEVENTH. 



This result may be attained in two ways : 1st, by giving the 7th to the 
soprano, which will render the close incomplete ; 



88. 



^3 



7 
22=3= 



2nd, by allowing the dominant seventn to enter on the accented part of the 
bar, while in the perfect cadence this position must be occupied by the chord of 
the tonic. 




Omission of 
one of the 
intervals of 
the chord 
of 7. 



The chord also often appears with omission of one interval, generally the 
fifth. 

The third is seldom omitted, and omission of either the root or the seventh 
would of course destroy the characteristics of the chord. 



90. 



a. 




6. 






C. 








-#L ^ 


/*T3 




— S — 


& 


53= 


— ?B 


m — S^ 




^O- - 




^ ! — ^; — 


— & — 1 — " — 


\y\) & vo 


S 














7 






7 




7 


■&■ 


7 


-o- 


<•> f ' -> 


i 




C^d. 




rj 




rj 




\<p). 


■ 










\js 


r.j 






r-> 












li i 











I. 



In the above example, at a, b, and d the fifth is omitted, at c the third, and 
in every case its place is siipplied by doubling the root. The new note then 
remains stationary, and forms a very intimate connection witJi the next chord, 
which then appears in its complete form. This could not be the case if the root 
of the chord of 7 were not doubled. (See Ex. 82.) 

Exercises. 



91. US 



=& 



^ 



-psz 






1 \— 



--,.-- 



2E 



ri= 



B 



^=&z 



RESOLUTION OF THE CHORD OF THE SEVENTH. 



39 



6 6 



3. 



m 



S 



- G P 



&- 



■ o - r-j 



:ot 



g? r-> 



£c=* 



^= 



122: 



-■*=* 



122: 



22- 



221 



4. 



(P$# 



e 

4 3 



B 

4 7 



6 

8 4 



£z: 



22= 



=22 



^=t 



zi 



221 



m 



pi 



6 7 

_4 #_ 

22 T 



« 6 



*' 



"g7~rrF-f 



S^EE 



=sT22= 



t=E 



s=2Z 



e 



^ 



6 7 

4 8 



ICC 



40 



INVERSIONS OF CHORD OF THE SEVENTH. 



Inversions 
of the chord 
of 7. 



CHAPTER V. 

OF THE INVERSIONS OF THE OHOED OF THE SEVENTH. 

The inversions of the chord of 7 are formed in the same manner as those of the 
common chord. The first inversion is formed by using the third as bass-note, 
and is called the chord of the sixth and fifth ( 5 ) ; the second by giving the fifth 

.6 v 

to the bass, this is called the chord of the sixth, fourth, and third (4 41; and in the 

V 3, 3' 

third inversion the original seventh becomes the bass-note, the chord is then called 
the chord of sixth, fourth, and second, or simply the chord of the second. 

(4 4 ). 

x 2, 2, 2' 



92. HI 



5 



6 
4 

8 

*3_ 



6 

4 
2 

g 



^=2= 



v 7 



As is the case with the inversions ot the common chord, these chords only 
depend on the position of the bass, the upper parts may then be arranged in 
various ways, for example : — 



93. 



f 








m 






n S> 


1— C= — 






n 






1 


U 




■g 






















I 


A 


















■ S 


^ 






1 










■£f 


Ss? | ' — 




g 


g^ 








1 


\\\l t-rfij 


~=*23" 




' rj" 


— "V-j 




iTJ 














6 — — 




6 
4 
8 


4 
8 


— 




6 
4 

a 


4 
a 


a 


CJ 





1 


fm\> 
























r -'G 


1 


l"l" 


























1 


*—' ^3 


























V 




1 — 




*—~ 





















etc. 



Their resoln 
tion. 



The resolution of these derived chords is founded on that of the original 
chord. 



RESOLUTION OF THE CHORD OF jj. 
Ch rdof 6 ^ n *^ e cnor d °f 5 the original seventh still forms a dissonance with the bass, 



THEIR RESOLUTION. 



41 



but in this case it is a diminished fifth (the resolution of which has already been 
explained). 



94. 



SE 



The resolution of the complete chord will therefore be as follows : — 







i*"j_ 


— . 


yj 


95. 


€£- 


".ft- 





-&rr 









G, 



That is, all the parts (except the root G) will have the same resolution as they 
had in the original chord. The root remains stationary, as it is not in the 
character of an upper or middle part to proceed by such large intervals as the 
root did when it appeared as bass of the original chord. 



RESOLUTION OF THE CHORD OF 



This chord contains between its component parts not only the interval of a choidof 4 
seventh (or its inversion, the second) but also that of a diminished fifth (or its * 

inversion, the augmented fourth). 



96. 



pO.- 



G^h 



Its resolution is therefore as follows : — 



97. E 



i=& 



m 



=a 



ss 



C: 



V, 



The bass, bemg the original fifth, is freely resolved. 



RESOLUTION OF THE CHORD OF 4 

2. 



This chord has the pecidiarity, that the dissonances of the original chord, viz. Chord of 4 
the seventh and the diminished fifth, can only appear in their inverted form as a 

second and augmented fourth. 



42 



INVERSIONS OF THE CHORD OF THE SEVENTH. 



The resolution of this chord is the same as heretofore, it must therefore be 
followed by the chord of 6. 



98. 



ES: 



C: 



v 7 



I 



a 



R 



9 



IC2C2J 



v, 



TABLE OF THE NATURAL RESOLUTIONS OF ALL THE INVERSIONS OF 
THE CHORD OF THE DOMINANT SEVENTH IN DIFFERENT POSITIONS. 



The Chord of g. 



99. 











._ 












r?-~ 


"^^O 


1/ 1 






~^- 


rj 








rj 






A. --K 






r5 




£2 










i(T» ,— > <* — 




















6 
6 


b£ 


'^^rr 


^j 






cu 








" £2 




§- 


6 
5 




e 

5 




R 


6 


-&- 


6 
5 


-O- 


AV 












r J 


CI 








II 


[W. 
























^— <S>— 






rj 




rj 




CJ 




rj 
















^— ~ 




*--"•" 






II 



0: V, 




I 



^ 



33E 



The Chord of 4. 

3 



SE 



~rT 7~ 



Z2ZT 



fe 



Z22~ 



4 
3 
^3 



~r?~ 



C: V, 



The Chord of 4. 

2 




100. 



* 



Exercises. 



~-?=l 



r=t 



:?z: 



zi 



e 

4 7 



2. 



Il= =J=: 



4 

3 6 



O-PZ 



EXERCISES ON CHORDS OF THE SEVENTH. 



m 



3^ 



6 8 7 



3. 



3 2 



■F-nr - 



e 

4 7 



^= 



22=^: 



z=t 



3 



* 



^ 



6 
6 4 3 



5. 



=?Z 



S 



2=t 



ZZ 



St 



r^-fs- 



/-: 



^ 



&zi 



^= 



6 7 

4 J* 



6. 



pt 



Ei 



tzzz 



3 



■3E 



^ 1 — 



4=± 



4 
3 



8 7 
6 8 — 



4 

3 6 



-rz>-& 



=?Z 



f=P 



ZZ 



g#=^ 



?2=& 



^ 



te 



#: 



6 7 

4 « 



9 



^t 



~?^~ 



8. 



5j 



^ 



=g= 



4 J 

3 3 6 3 



6 7 

4 Jf 



:g=P= 



( 44 ) 



CHAPTEE VI. 



OF SECOND AEY CHORDS OF THE SEVENTH. 



Secondary 
chords of the 
seventh. 



Besides the chord of the dominant seventh, other chords of the seventh are 
possible on every degree of the major and minor scale. These are called 
secondary sevenths, and are all formed by adding a new note, distant a seventh 
from the root, to any of the common chords already found. Their relationship to 
any given key is certainly undeniable, but not so decided as that of the dominant 
seventh. 



101. 



P 



In Major. 



I 7 ii, 

In Minor. 



E§E 



m, IV, 



vi, vn° 7 



I? 



-St- 
ill'* 



rv 7 



VI* 



TO". 



The dimi- 
nished 
seventh. 



We find here harmonies which have a somewhat harsh and foreign effect, 
because, as has already been observed, their relationship to the scale is not so 
distinct as that of the dominant seventh. They are therefore less frequently 
employed, but are nevertheless well adapted to give variety to the harmonic 
progression. 

One of the secondary sevenths, that on the seventh degree of the minor scale, 
contains an interval which has not hitherto been spoken of, namely, the diminished 
seventh. This interval is smaller by one semitone than the minor seventh, from 
which it may be formed by chromatically raising the root, in the same manner 
that the diminished fifth was formed from the perfect fifth. (See p. 20.) 



102. 



j 

P 



Minor Seventh. Diminished Seventh. 



SECONDARY CHORDS OF THE SEVENTH. 



45 



Like all diminished intervals it is a dissonance, and therefore requires to be 
resolved. Its resolution and treatment will be explained hereafter. 
The secondary sevenths may be classified thus : — 

1. Major common chords with major sevenths : — 



103. 



In Major. 



In Minor. 



C: 1 7 



IV, 



VI 7 



2. Minor chord with major seventh : — 

In Minor. 

Not used in its fundamental form. 



m 



a: i 7 



3. Minor chords with minor sevenths :- 

In Major. _ In Minor. 




vi, a : iv. 



4. Diminished chords (chords of diminished fifth) with minor seventns: — 

In Major. In Minor. 



i 



w 



C : VII°, 



5. Diminished chord with diminished sevenths :— 



In Minor. 
s> 



8. Augmented chord with major seventh : — 

In Minor. 

■W — $ gl : H Seldom used. 

*a: T?I'» 



46 



OF SECONDARY CHORDS OF THE SEVENTH. 



Resolution of 
the secondary 
sevenths. 



Downward 
resolution of 
the third. 



EMPLOYMENT OF THE SECONDARY SEVENTHS OF THE MAJOR SCALE. 

Whether the interval of the seventh (or its inversion, the second) be major, 
minor, diminished, or augmented, it will always form a dissonance with the root, 
and as such will require a resolution. 

This resolution will be the same as that already given to the»dominant seventh, 
t. e., the seventh will descend one degree, while the root proceeds a fourth upwards 
or fifth downwards. The progression of the principal notes of the chord being 
thus found : — 



104. I JizgZ^ 



the remaining intervals require no new rule ; the third ascends one degree, 
while the resolution of the fifth is free. 

— — b - c - _ 



105. 






^ 



E3E 



ES 



=ss= 



IZ2I 



C: 1 7 



IV. 



II, 



V. 



The exceptional progression of the third shown at b in the above example is 
in order to avoid the covered octaves which would otherwise occur between tenor 
and bass; and which would be the more objectionable that the tenor at b proceeds 
a whole tone, f-g, instead of half a tone as at a. (see p. 18.) 

Whether, however, it will be preferable to double the leading note in the 
chord which follows the chord of the seventh, as at c in Ex. 105, or to employ 
the following hidden fifths, will depend upon circumstances. 



106. 



■Jt g-j . 


^~a 


(S 


~~ — s> 


m — cS — 


~~~& — 




■ & 


if 








r -' 1 


VP )• _-, 






1 


VL^ <-> 






1 











C : n, V. 

The natural resolution of the secondary sevenths on each degree of the major 
scale is therefore as follows : — 

On the 1st Degree. With omission of the 5th. 



107. 



E2g 



W 



it 



22= 



IV. 



~rzr 



SE 



^ 



etc. 



32Z 



CHORD OF SEVENTH ON THE SEVENTH DEGREE. 



47 



On the 2nd Degree. 



With omission of the 5th. 




ii, V. 

On the 3rd Degree 



With omission of the 5th. 



-<§- 



5E 



HI, 



On the 4th Degree 

(This resolution is seldom used.) 



Without the 5th. 



IV ? vir 

On the Gth Degree. 



Without the 5th. 



fP 

(In 



js: 



3S 



£Z 



EH^S 



"«7 



etc. 



^ =J 


'S' 

-^> 


— -F3 — 

rS> 1 


S> 

1 — s — 

f3 


— s — 


— e 

— & 


(?¥. e. 




(S> 




— e> — 





<^ 











— e — 



etc. 



etc. 



On the 7th Degree. 



WiTnouT the 5th. 




ON THE PECULIAR RESOLUTION OF THE CHORD OF SEVENTH ON THE 

SEVENTH DEGREE. 

In the above table the same resolution has been given to all the chords of chord of 7 on 
seventh, including that on the seventh degree, (i. e., in each case the bass proceeds . leading 
a fourth upwards or a fifth downwards). A more usual progression, however, 
of this chord is that founded on the resolution of the chord of diminished 
fifth, from which the chord of seventh now under consideration is derived. 



48 



OF SECONDARY CHORDS OF THE SEVENTH. 



Its resolution. The following example will show that the tendency of the chord of diminished 
fifth towards that of the tonic is not only unaltered, but even rendered more 
decided, by the addition of the seventh. 



108. 



a. 






»■ -«-- 


— T? 


a. 




b. 




U ■»* 


fj 




~~irifTS 










/] '^ 


rJ?-j 


g 


j. <J 










fa\ — 












rj "- 




1(11 








& ~~~ 






"- S 


U 






£> --S- 


CJ ■-» 


tm\' 














^ _i 7 


\r>- 










<V 




\ — 








& 


1*5 




. <Zl 














' ' «—"" 



Observe that when the chord appears in the above position, either the third in 
the succeeding chord must be doubled (see Ex. 108 b) to avoid the consecutive 
fifths shown in Ex. 109 at a, or the third in the chord of seventh must take a 
leap as shown at b. 



109. 




This cnord has the peculiarity that the above is its only satisfactory position, 
and that all others, where the seventh is not at the top of the chord, are uncertain 



The best 

position of 

the chord of 

7 on the lead- and indistinct in their effect, if not entirely useless 

ing note. 



110. 



p 



SE 



i g zn s 



T ^~ 



w 



ZZZ1 



Free progres- 
sions of the 
third and 
fifth of the 
chord of 7. 



The intervals of third and fifth in the chord of the seventh can also have 
other (free) progressions besides those already allotted to them. A free progression 
of the third will often render the general progression of parts more independent. 
For example : — 

Bad. _£2_ _ 



111. 



P 



>g 



13 z 



~52l 



ZZ2Z 



S 



r22i 



PREPARATION OF THE SEVENTH. 



49 



The progression of the soprano in the second bar of the above example is not Progression ol 

, . . the tritone. 

good on account of the interval f-b forming an augmented fourth. This interval 

is also called the tritone, because it contains three whole tones. It will be more 

fully mentioned hereafter. 

A free progression of the fifth is only possible when the progression of the 

bass differs from that hitherto employed. Examples of this will be found 

hereafter. 



PREPARATION OF THE SEVENTH. 



The harsh effect produced by the sudden appearance of many of the disso- Preparation 
nances, and especially of the secondary sevenths, renders a careful introduction intervals. 
of them necessary. 

This introduction is called the preparation of a dissonance. A note is said to 
beprepared when it has already appeared as a consonance in the foregoing chord 
and in the same part. The already-mentioned connection of chords is therefore 
nothing more than preparation, as in the following example it may be said that 
the C in the soprano in the second chord is prepared by the C in the first. 



112. 




The preparation of the seventh may take place in the following or any similar Preparation 

of the seventh. 

manner : — 



113, 



) 



I 



£=> 



-S^ 



hidflife^y 



li^gi 



s : 



JTJ 






J 



H 



-J J* I e'c. 



W 



f=c 



id 



?2 






C: V. I, IV. V. I, IV. IV. ii, V. I. ii. V 7 I. I. vijn. IV.vu°,I. 



In each of the above examples the note which is bound to the next following 
by means of a slur '"" ""■, forms the preparation of the seventh. 

In the construction of such preparations the following rules must be Rules for 

observed : — Preparations. 

v l) The preparation must fall on the unaccented part of the bar (arsis). 



50 



OF SECONDARY CHORDS OF THE SEVENTH. 



(2) It must be of at least equal duration with the seventh by which it is 
followed. It may also be longer, but never shorter. 



114. 



Good. 



) 

X 



9 



i 



m 



st 



~3SL 



-*T 



Bad. 



=^= 



^2= 



^ 



=P=C 



Entrance of The chord of dominant seventh, however, being less foreign to the key than 

the dominant , , , . °. , . 

seventh with- the other sevenths, does not always require preparation. The note forming the 
Son?"*"" 1 interval of seventh in this chord may be freely introduced, but in this case the 
root of the chord should be already present in the previous chord, in order to 
preserve the progression of parts pure and free from harshness. 



115- 




Entrance of 
the chord of 
7 on the 
leading note 
without pre- 
paration. 



In each of the above examples the root of the chord of dominant seventh is 
present in the preceding chord (in the alto) ; the seventh is therefore allowed to 
appear without preparation. 

The chord of seventh on the seventh degree of the major or minor scale 
may also be used without preparation. 

Exercises. 



116. ffls 



r-: 



==z 



e 

47 



g 



^=P= 



^2= 



T=z- 



Szzzlz 



23i :trr 



i=t 



?z: 



m 



±=pr. 



t^=g- 



z2=^: 



fa-^^p- 



M — i- 



^ 



E± 



=£2- 



=& 



-=$—&- 



CONNECTION OF CHORDS OF SEVENTH. 



51 



THE CONNECTION OF CHORDS OF THE SEVENTH ONE WITH ANOTHER 



Hitherto every chord of seventh has been resolved into the common chord of Resolution of 

J one chord of 7 

the f ourth degree above its root. A second chord of seventh may, however, serve into another, 
as its resolution, the root of the new chord being likewise four degrees above that 
of the first. In this case the third in the first chord of seventh will remain 
stationary, in order to form the necessary preparation of the seventh in the 
succeeding chord. For example : — 



=15= 



=£2= 






iSE 



117. 



=g= 



7 

=22= 



22= 



v 7 



IV. 



Here the third of the chord of dominant seventh remains stationary, and How effected, 
prepares the seventh in the chord of seventh on the first degree. All the other 
intervals are resolved as usual. 

The peculiarity of this progression is, that in one of the two chords of seventh 
the fifth will always be omitted, and in a sequence of sevenths, i. e., when several 
chords of seventh follow each other, this omission of the fifth will take place in 
every other chord. For example : — 



118, 



^S= 



+ 



22= 



=p=^sp 



22; 



22Z 



teJ— l 



C - > f=z 



22= 



=!=# 



I I 



■J ^ 



§3 



22= 



3===" 



23= 



=t= 



22= 



=f^ 



m 



;j_ 



=& 



±-± 



2== 



H, V 7 I;; 



IV, 



=J= 



etc. 



IV7 vn° 7 in, vl, n, V 7 



Exercises. 



1. 



119. g§g 



2. 



2Z 



A- 



T3 r 



£ 



=^: 



;6z= 



22: 



m 



6 
6 4 

2 



a 



3. 



m 



'-2 2 _l 



S 



£=====ffi 



St 



22Z 



=^= 



IQ_ 



^=22: 



22: 



e2: 



4. 



E^=3 



6 
6, 6 



3 



3 



?3=g: 
t=t=: 



33: 



22: 



^t 



ZZ 



ffi 



52 



OF SECONDARY CHORDS OF THE SEVENTH 



EMPLOYMENT OF THE SECONDARY SEVENTHS OF THE MINOR SCALE 



Secondary 
sevenths of 
the minor 
scale. 

The chord of 
7 on the first 
degree. 



The use of the secondary sevenths of the minor scale is not so general as that 
of the sevenths of the major scale. Many of them are either uncertain and 
ambiguous, or in their resolutions produce harsh anti-melodic progression of 
parts. With these last may be classed the chord of seventh on the first degree of 
a minor scale, which, as will readily be seen from the following example, cannot 
well be employed on account of the progression of an augmented second caused 
by its resolution. 



120. 




On the second 
degree. 



The chord of seventh on the second degree is resolved into the chord of the 
dominant, and is very generally used. 



121. 



-p 1 




I — ~ — ' 


rj 


— g - 


rjrj 


1 <s — 


r-Ji 


X 
















Im r r> 




<^ 


ft — 


rJ 


+fc — ' 


rj 


•It, — • 


\M) /*.> 


8S 


<V> 


ft- 




TC^ 




rfe? 


U 


7 




8 


ro . 




J2. 


C3 


w. 














E£- 


—& 































etc 



On the third 
degree. 



A resolution of the chord of seventh on the third degree is not impossible; it 
is however ambiguous, and belongs rather to C major than to A minor. (See 
altered chords, p. 68.) 

rr^ i ~ „ fe- 



3 



ES^ 



Z2PI 



122. 



a: III'* 



VI. 



On the fourth The chords of seventh on the fourth and sixth degrees are seldom employed, 
d^ d e^ M thei* resolution occasions harsh progressions. This will be perceived from the 
following examples : — 

Good. 



s 



±z 



~&L 



=3S 



ZZ2Z. 



=s= 



=3- 



123. 



vu° 



"W- 



^ 



EMPLOYMENT OF SECONDARY SEVENTHS OF MLNOR SCALE. 



as 



i 



~(T7~ 



ESF 



~cr 



ESE 



-Sz 



f): o 



a: VI, 



The seventh degree of the minor scale carries a very important chord, known On the 

as the chord of diminished seventh. Its resolution, as in the case of the chord degree • 

of seventh on the seventh degree of the major scale (see p. 47), is founded on ^™^ hed 
the natural upward tendency of its root, which is the leading note of the scale. 



seventh. 
Its resolu- 
tion. 



124 



■m 



m 



Thus, while the root rises and the seventh falls one degree, as is usual with 
diminished intervals, (see p. 20), the third and fifth proceed as in other chords of 
the seventh, and the resolution of the whole chord takes place as follows .• — 



125. 



f 



5£ 



Bad. 

— &- 



=g 



W^ 



¥= 



^ 



It is also possible for the third of the chord of diminished seventh to descend 
by a leap into the fifth of the -ensuing chord, as in the case of the chord of 
diminished fifth (see p. 22). 



126. 



m 



:=?= 



The chord of diminished seventh, being the least harsh of all the secondary 
sevenths, does not reqxure preparation. 

The student is here recommended to read over again the rules relating to the 
chord of diminished fifth (see p. 20, &c), on account of the great similarity 
which exists between that chord and the chord of diminished seventh, both as 
regards its position in the scale and its treatment. 



54 



OF SECONDARY CHORDS OF THE SEVENTH. 



Exercises. 



127. p ^B 



^: 



-■&=i-n 



& 



-P2 



--£*- 



2. 



Z2I 



m 



7 
68 



PZ 



:& 



4 

6 2 6. 



e 



z=£ 



6 7 
6 4 8 



1 1 1 — ig>-— «-« 



3. 



7 6 

7 « * 



iHl 



^ 



^ 



1=2: 



?= 



f 



7 

7 * 



4. 



B 



:& 



4 
2 e 



S 



^21 



^ 



^ 



8 7 

6 4 8 



3=z 



22: 



In No. 2 of the above exercises the chord of seventh on the third degree of 
the minor scale is introduced. It is, however, strictly prepared, and on that 
account will not appear harsh or unnatural. 



f 66 ) 



CHAPTER VII. 



OF THE INVERSIONS OF THE SECONDARY SEVENTHS. 



The inversions of the secondary sevenths in manor or minor give the same Inversions 
derived chords as those of the dominant seventh, viz., the J? ^ and 4 



5, 3, 



of the second- 
ary sevenths. 



128. 



i 



w 



-z?&- 



Z£ 



4 
3 



^ 



=« 



SE 



C: 



IV. 



No new rules are required for the resolution of these chords. In the resolu- Their resolu- 
tion of the inversions of the chord of seventh on the seventh degree, care is on * 
necessary to avoid the consecutive fifths which are otherwise apt to occur. 



129. 



Bad. 



to A 



-g^r 



_g^ 



w± 



^ 



:§=z=cz: 



221 



m 



C : vn°, I. 



All the above inversions are available, that of the 4 being however least 

used, as its resolution, (the chord of 4 ) can be employed but seldom, and then 
only as a passing chord. The inversions of the diminished seventh require a 
similar resolution to the foregoing. 



130 



i 



~g& 






se 



6 



4 
3 



zSs; 



4 
2S 



IS 

a: 



u 



2=C 



■LGL 



E5S 



The imsatisfactory resolution into the chord of 4 of the inversion 4 

again affords a reason why this chord should seldom be employed (see preceding 
paragraph). 



56 



OF THE INVERSIONS OF THE SECONDARY SEVENTHS. 



Best position It has already been remarked (p. 48) that the only satisfactory position of the 

sions of the chord of seventh on the seventh degree in major is that with the seventh at the 

leadin*' note 16 to P °^ ^e cnor( l 5 tae following positions of its inversions are also more satis- 

of the major factory in their effect than those given in Ex. 129, because the seventh is here 

SCtllG, 

retained in its original position above the root instead of being inverted and thus 
forming a second. 



131. 



®£ 



£S 



C : vn° 



IZ2Z 



^ 



6 
5 



ESE 



This is however not necessary in the case of the diminished seventh ; in the 



Position of 
the inver- 
sions of the inversions of this chord the seventh may He either above or below the root, the 

diminished ». , . .., , . ... 

seventh. wiect in either case being similar. 



Exercises. 



132 -Hte 



e e 



^- : -^- 



=& 



3=2: 



z± 



ffi^E 



W=^f=\ 



pz 



3=^: 



(§Ei 



=^ 



4 



-&-S -- 



H „ \M 



-?=£ 



CJ [ 



l=t 



=£2- 



-^ 



-rz)~ 



rsz: 



-2 6- — -2 e 



p==^T 



m 



6 6, 



I 



=£21 



rs: 



E± 



2Z 



zi 



?=: 



ri-&- 



5-6 



rt 



g-g2 



^4 



=z£ 



s 



?= 



2=£ 



6. 

m 



S/-S2 6. 

22q: 



¥ 



e ^ 



S 



a 



zz 



-^>—rr 



z=fc 



:z=£ 



& 



22 



3±= 



^ 



g 

4 
3 



8. 



3 



2=£ 



e 



ips: 



JSC 



B 



— ^ 2 J 



S 



=ci 



^ 



H^ 



f^ 



Z!=t 



m, 



4 
3 



« e 

» 5 

tS> 1 



^ 



7 6 6 7 

#4 4ff 



=& 



^ 



E^ 



£ 



-f=-L-S>-l-(^ 



=pz 



3^ 



Z± 



^: 



2Z 



10. 


6 

6 6 


4 
7 8 


% 2 


6 6 


. 1 , 


6 


6 

O * - 




/•v 1 r j 






"p- f3 " 






,-J 


f~ 1 




teJL- (?^-g>-1 — 


'P P" 






S_^ 


-sUJ- 


— IS 


-^ r- 


— s>— 


^-^p y I — 1 — 


1 1 J 




— 1 1 


1 


^-^jc^ 


i.r ' 


y=H 





( 57 ) 



CHAPTEK VIII. 

OF THE CONNECTION OF THE CHOEDS OF THE SEVENTH 
WITH CHOEDS OF OTHEE DEGEEES. 



The progression of the interval of the seventh depends entirely on that of Various free 
the root. Hitherto the latter has always proceeded a fourth upwards or a fifth the seventh. 
downwards ; under these circumstances the seventh, as has already heen shown, 
descends one degree. The progression of the root may however be such that the 
seventh shall remain stationary, or even ascend, for example : — 



133. p 



-^nztz 



ES 



*£ 



3^ 



The above example proves the possibility of connecting the chords of seventh 
with other chords than those hitherto employed. The following are examples of 
a few methods of effecting this : — 

(1). The connection of the chord of dominant seventh with various The seventh 
common chords (excepting that of the tonic,) the seventh always descending. escen ®" 
(a) 



Connection with the chord of the sixth degree. 



In Major. 



In Minor. 



134. 




SE 



Tg?: 



SE 



S 



^E 



h 



~^ 



Tzr 



VI. 



This progression is very often used. 

The effect of the inversions of the seventh under similar circumstances is less 
decided than that of the chord itself ; they are therefore seldom used. 

In Major. 



135 



■ I 



e 

6 



In Mi>ior. 



a 



•■&&. i 



r ^ = 



v 7 



"Z3~ 



^M 



(b) Connection with the chord of the third degree. 
In Major. Better. 



136. 



rS2S2T 



<S>- " fc j — — ^g 



C: V 



C~ 



58 CONNECTION OF CHORDS OF SEVENTH WITk OTHER CHORDS. 

This progression becomes still more effective if a modulation towards A minor 
be introduced. 



137 



m 

C: V 7 



6 



\P- 



The dominant seventh may also be connected with the chord of the third 
degree in minor. The latter chord, however, being itself a dissonance, will also 
require to be resolved. 

In Minor. 

138. ~ 




The seventh 

remaining 

stationary. 



(2). The connection of the chord of dominant seventh with various 
common chords, the seventh remaining stationary. 
(a) Connection with the second degree. 



In Major. 



Not used in Minor. 



139. 




(b) Connection with the fourth degree. 



In Major. 



In Minor. 



■1 



140 



w. 



=222; 



§£E 



IZ2I 



^3- 



a 



3E 



C: V, 



rv. 



ESE 



The chord of dominant seventh may also be connected with other chords o£ 
the seventh on different degrees, for example : — 



141. 



Pi 



E£ 



IZ2I 



VI 7 



V, 



ni 7 



fe 



V 7 a:*V. 



etc. 



With modula- 
tions. 



If modulations are introduced, many new connections of chords of the 
seventh with one another become possible, for example : — 
(a) With the seventh descending. 



142. 



i 



J2. 
— <^- 



9 



m 



pg 



1 



£=5 



C: 



C: V 7 b: vu°, a: V 7 F: V 7 a: V 7 G: vu° 



CONNECTION OF CHORDS OF SEVENTH WITH OTHER CHORDS. 



59 



143. 



(b) With the seventh remaining stationary. 



&n 



22 



§i£E§Ef§=p± 



C: 



Eb:V 7 C:V 7 Bb: V 7 a: V 7 C : V 7 a: V 7 G : V 7 



(3). The connection of the chord of the dominant seventh with various The seventh 

ascending. 
other chords, the seventh ascending. 

It will be possible for the seventh to ascend — 

(a) when the root proceeds to that note into which the seventh would 

ordinarily resolve itself, for example : — 

a. b. 



144. 



-Q 




yr . i*j 




fA G ,X 




Vif rj ■ — ■ «-> 


rj*> . — 


tr 


7 6 


Hi 
7 


6 


/m\' f 


i-J 


(rJ. 


■ <tj 


IT? 


VL> 









Here the root of the dominant seventh proceeds to E, which would be the 
ordinary resolution of the seventh F ; this latter must, therefore, ascend, in order 
to avoid the covered octaves shown at Ex. 144 b. 
(b) When the root remains stationary. 



145. 



ZZ2Z 



zt2i 



m 



3E 



:S^B 



In this case, however, the seventh must lie at a distance from the root ; *he 
following progression is therefore faulty. 



146. 



^ 



IZ2I 



(c) When the seventh itself is chromatically raised for the purpose of 
modulation. 



147, 



i 



¥ 



te 



tr *S- 
C : V, G : V 7 C : V 7 G : V 7 



1- 



m 



C : V 7 e : vn° 7 



60 CONNECTION OF CHORDS OF SEVENTH WITH OTHER CHORDS. 



(d) When, in the case of modulation, the bass moves in contrary 



motion. 



148. 



W 



C2_ 



SSEE 



j=zk. 



$ 



i_ 



ggl^g^ 



d: v 7 C: V 7 b[?:vn 7 a:v 7 d:vn° 7 C: V 7 F : V 7 



Jcceptive 
cadence (7k- 

ganno). 



In all the above examples, the ear is as it were deceived by the substitution of 
some other chord for the chord of the tonic, which would be the natural resolu 
tion of the dominant seventh. On this account, a progression in which the chord 
of dominant seventh is followed by some other chord than that of the tonic, 
is termed the deceptive cadence (Inganno). 



149. gig: 



Exercises. 



6 

5 4 7 



-T3~ 



■m 



?= 



3=z 



-g~ 



~rzr 



:^=P2: 



W^ 



3. 3 



6 7 

4 » 



(h 



fe 



^t 



^t 



Z2. 



:^2=fc 



2± 



z± 



4 
8 



g 



4. 



6 7 

4 Jf 



=f=2 



3P 



d I 



22. 



:s£ 



23; 



2±^ 



Z£ 



2i 



^ 



zi: 



^d 



^Eg? 



6 7 

4 » 



6 

4 7 



ict 



iza= 



1% 



:?=: 



z± 



^ 



IZ2I 



CONNECTION OF THE SECONDARY SEVENTHS WITH OTHER CHORDS OF 
VARIOUS DEGREES OR IN DIFFERENT KEYS. 



It would be equally impossible and unnecessary to give examples of all the 
Connection of connections of the secondary sevenths with other chords. The following are, 

secondary J a 

sevenths with however, a few of the most useful. 

(a) With the seventh strictly resolved. 



The seventh 
descending. 



150. 



-&- 



9 



IZ2Z 



C: 



n 7 



-s>- 



3SE 



* 



iEC 



m. 



a:V 



23 _ 

c: n 7 



^ 



e : V, 



IV. 



=£=<£ 



i=iiO=s£==ta 



m 7 



F:V 7 C: 1V 7 G:V 7 



3-" 

a: u° 7 



ISC 



etc. 



III'. 



VI. 



CONNECTION OF SECONDARY SEVENTHS WITH OTHER CHORDS. 61 
(b) With the seventh freely resolved. 



Bad. 



151. 



5E 



ito 



TSL 



^ 



-feF 



» 



* 



$ 

TF 



17 <-* -cy ^ -£J- 

c: n 7 o: vn.° 7 c : n 7 a : "V 7 c : n 7 a:vu, 



etc. 



The se^ euth 
ascending. 



» This example is objectionable on account of the so-called false relation between soprano and 
bass. The false relation will be explained hereafter. 



(c) With the seventh remaining stationary. 



152.: 



>=g=S 



3E 



32: 



=3= 



^ 



'-&- 



S 



-<^?i 



etc. 



The seventh 

remaining 

stationary. 



IV. c : n 7 



c: n 7 



V. 



The progression shown in the last bar of the above example is often employed. 
It can scarcely be considered as a free resolution of the seventh, as the real 
resolution is merely delayed by the introduction of the chord of | and then takes 
place in its ordinary form in the next chord. 

In the same manner the resolution of the diminished seventh is often delayed 
by the interposition of the chord of 4 . thus : — 



153. 



6 b 

, ,7 b 1,4 

itetei 



^iS^ 






8 1 

4 . 



*=fc 



221 



ra°, C: I. 



\rz, i ^- 



Delayed reso- 
lution of the 
diminished 
seventh. 



Exercises. 



154. gg^jE 



7 
6 8 



^ 



=1= 



:s=fc 



T= 



=^= 



^ 



^ 



^= 



rg: 



6 
7 6 



w& 



■ v F 



: g— fv. 



Z2=t= 



^ 



2± 



3. 


8 


6 

B 


6 
4, 


7 


7 




B 




7 


6 


6 
5. 


e 7 

4 # 




/■v ! 


| 


| 


, 


' | 


| 








<ZL 


-S>— 


-rJ- 


=S) 


r- 1 - 

-1 — 


— 4- 


-=*— 


—&— 


=3- 


-rr^ 


-<S^- 


<*■-> 


« 



4. 



3E 



4 

2 



B 7 

4 # 



± 



E^fe 



^ 



^= 



=t 



Many of the above exercises would have been smoother and more melodious had it been allow- 
able to introduce modulations. At present, however, we have not treated of modulations, 
and on this account many of the progressions exemplified in the foregoing chapter could not 
be introduced into the exercises. 



( 62 ) 



Chords of 9, 
11, and 13. 

Their defini- 
tion. 



Construction 
of the chord 
of 9. 



CHAPTEK IX. 

OF CHORDS OF THE NINTH, ELEVENTH, AND 

THIRTEENTH. 

The views which may he entertained of the ahove chords are various, hut they 
all tend to one practical result. It may he taken for granted that these are 
either real chords, such as the chord of seventh, in which case they must be con- 
sidered and treated as such, or that they belong to the list of suspensions, or else 
occur accidentally when one or more parts remain stationary. 

In the first case their explanation, and especially that of their inversions, 
would be extremely prolix, and moreover the chords themselves would often be 
difficult to recognise, inasmuch as in four-part harmony one or more of their 
intervals must always be omitted. If, however, considered as suspensions or 
accidental chords, their explanation becomes very simple. In order to obtain a 
clear insight into their nature, we will now proceed to examine their con- 
struction, &c. 

By adding to the chord of dominant seventh a new interval, distant a ninth 
from the root, a new chord is formed, known as the chord of dominant ninth. In 
the major scale the ninth is major, and in the minor scale minor. 

In Major. In Minor. 



—Q & p & n 

i55. a==i =H^ig^fl 



Ita prepara- 
tion. 



In pure harmonic progression it is necessary that either the ninth or the root 
should be prepared ; the following example, therefore, in which both root and 
ninth enter freely, is objectionable on account of its want of connection. 



156. 



J 



ZE21 



The preparation may take place as follows : — 
_g=T~ 



157 






:9z 



k 



^m 



9 

7 

=P= 



-<=>- 



r= 



=f=== 



CHORDS OF NINTH, ELEVENTH, AND THIRTEENTH. 



Whether the above combinations are to be considered as suspensions, or other 
accidental chords, will be considered in a later chapter. 

Many theoretical works treat also of the formation of other chords of the Secondary 
ninth, called secondary ninths ; this is, however, quite unnecessary, for inasmuch cessary. 
as they can never appear without preparation, their treatment, resolution, &c, will 
be in every respect similar to that of suspensions (see chapter on suspensions). 

Chords of the eleventh and thirteenth are still less worthy to be considered Chorda of g 

real chords. , }? 

and 11 



11 



158, 



P 



n 

7 



13 
11 

9 

7 



S 



-§:- 



'■& 



It is evident that they can never be employed in pure four-part writing, since Cannot be em- 
the necessary omission of some of their intervals would completely alter their parts. 
nature, and transform them into simple suspension, thus : — 



159 



jZtl 



=St 



:g=3 



£1 



& & 



3=£ 



or, 



■&. 



And even in compositions in six or eight parts, where they might appear in their 
complete form, then - character and treatment will still be that of a suspension, 
while in fcne free style, where they may also occur without preparation, they must 
be considered as passing notes (see chapter on suspensions). 



( 64 ) 



CHAPTER X. 

OF THE CHROMATIC ALTERATION OF FUNDAMENTAL 
HARMONIES (ALTERED CHORDS). 



Chromatic 
alterations 
producing 

modulations 



The chromatic alteration of one or more intervals of a fundamental chord pro- 
duces one of two different effects : it eitner ciuses a modulation into some new 
key, or gives an entirely new form aoa construction to the chord itself. If, for 
example, the major common chord he chromatically altered, thu*- 



16 °- ^^pppEgf=B 



Chromatically 
altered funda- 
mental har- 
monies. 



znodulations will be effected, at a ("by means of the chord of diminished fifth on 
the seventh degree) into D major or minor, or (by the chord of diminished fifth 
on the second degree) into B minor; at b into C minor, and at c (by the chord of 
diminished fifth on the seventh degree) into T>\> major or minor. 

The following chromatic alterations of the same chord will not effect modula- 
tions, but the nature of the chord itself will be totally changed. 



161. 



l^^jgplgiigESgjggfei 



Various kinds 
of intervals. 



The above combinations contain several intervals which have not hitherto beui; 
met with. It will therefore be necessary, before proceeding farther, to consider 
how many different kinds of intervals are possible, and what is their harmonic 
value. It has been stated in the chapter on intervals (p. 5), lstly, that unisons, 
fifths, fourths, and octaves, which are formed of the notes of a diatonic major 
scale, and which have the first degree of that scale for their lower note, are called 
perfect ; 2ndly, that seconds, thirds, sixths, and sevenths, formed in the same 
manner and under the same conditions, are called major ; and 3rdly, that minor 
intervals are formed from major by chromatically lowering the upper note one 
semitone. To these rules may now be added the following : — 



ALTERED CHORDS. 



65 



(1). If the upper note of major and perfect intervals be chromatically Formation of 

augmented 
intervals. 



raised one semitone, augmented intervals are formed. 



# 



Augmented. Augmented. Augmented. Augmented. Augmented. Augmented. 



162. 



^js- | 



Unison. 



Z2 - 

Second. 



'± 



feE 



:=- 



Fourth. 



Fifth. 



Sixth. 



Octave. 



(2). If the lower note of most of the perfect and minor intervals be Of diminished 



chromatically raised one semitone, diminished intervals are formed. 



intervals. 



Diminished. Diminished. Diminished. Diminished. Diminished. 



I 



$=tpF 



Ja: 



Seventh. 



Third. 



Fourth. 



Fifth. 



Octave. 



N.B. — Augmented thirds, sevenths, and ninths', as well as diminished unisons, seconds, sixths, 
and ninths, have no harmonic value. 



Of the augmented intervals given in the above example two have already been 
met with, viz., the augmented fifth (see p. 24) and (in the form of an inversion 
of the diminished fifth) the augmented fourth (see pp. 20 and 32). 

Two also of the diminished intervals shown above have already been employed, 
viz., the diminished fifth (see p. 20) and the diminished seventh (see p. 44). 

All augmented and d i minished intervals, as has already been observed, are They are d ; s . 
dissonances. 

Augmented intervals, when inverted, become diminished ; and diminished in- 
tervals, by inversion, become augmented. 

This will be clearly seen from the following Table of Inversions, which will 
also serve as a recapitulation of what has already been said on this subject at 
p. 6. 



sonances. 

Their inver- 
sions. 



66 



CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 



00 

o 

'go 

M 

c 

H 

n 




CO 

CD 



■CS 



a 



ALTERED CHORUS. 



67 



The augmented octave, and the major or minor ninth, have not been included 
in the abo\e table as they cannot be inverted in the octave, since in them the 
upper note would never become lower than the lower note. This will, of course, 
be equally the case with all intervals greater than a perfect octave. 

It will be remembered that the climinished fifth was formed (at p. 20) by 
chromatically raising the root of the perfect fifth, and not by lowering the upper 
note, which would appear to have a similar effect. The reason of this may now 
be understood from the foregoing table of inversions. For, since the augmented 
fourth C-F$— 



The augment- 
ed octave and 
major and 
minor ninth 
cannot be 
inverted. 

Formation of 
the dimi- 
nished fifth. 



i 



is formed by chromatically raising the upper note, F, it follows that its inversion, 
the diminished fifth, Ff-C— 



i 



p=p 



will also contain a chromatically raised F, being in this case the lower note of the 
interval. Any other diminished fifth in which the upper note should have been 
lowered, such as 



m 



•i 



will therefore belong to a different scale, that of C[?, and will in reality have been 
formed by raising the lower note F by means of a tj thus : — 



m 



fe 



gr"Pi? \rr . 



We may now return to the chromatically altered chords shown in Ex. 161. 
Of these combinations, the two marked c and e can alone be considered as real 
chords. The others have no harmonic value, and can only be used as passing 
chords. 

The chord shown in Ex. 161 at c has already been met with on the third chord of the 
degree of the minor scale (see p. 24), and is termed the augmented common j^™ 611 
chord. 

Its employment is, however, much more general in its present position, as 
common chord of the first, fourth, or fifth degree, with its interval of fifth chro- 
matically raised. 

The resolution of the dissonant interval of this chord (viz., the augmented Its resolution, 
fifth) is one degree upwards, as is the case with all augmented intervals (see 
p. 20). 



68 



CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 



Its inversions. 



The following example will show the formation of the augmented conuacr. 
chord by means of the passing note G §, as well as its resolution : — 

b. 

3E 



164. p 



* 



m 



SE 



^S 



The inversions of this chord are also available : — 



165. 



m 



ES 



6 

S 



3H 



Eli: 



r. 



IV. 



IV. 



V*. 



IV. 



etc. 



TO" 



Its appear- Although these chords are generally used either as passing chords (as in 

preparation! Ex. 164 a) or with the fifth strictly prepared, yet in rapid changes of harmony 
they may also appear without preparation. 



166. 



P 



J - v J - ,K 



W£ 



w 



4 



The chord of To the three augmented common chords on the first, fourth, and fifth degrees 

fiftfi with the ma y be added the respective sevenths belonging to those degrees. Of these 
addlt tk a combinations the one most used is the dominant seventh with augmented fifth. 



167. 



P 



IS: 



~rzr 



fe 



-?rr 



a: 



==SE 



S 



m 



7 
6S 

zSz 



fc 



~CTI 



C: V, I. 

A combination of the chord of seventh on the first degree with the augmented 
fifth is also possible. (See p. 52.) 



168. 




CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 



69 



The augmented chord on the fourth degree with tie addition of the seventh 
is, however, very seldom used. 



169. 



1 



jczi 



¥ 



ZZ2Z 



7 

,5ft 



'HE 



J&- 



C : 1V 7 vn°. 



331 



~T7 ~ 



ZZ2Z 



«M 



m &. 



6 



6 
4 
2 



Efe 



In all the above examples the ordinary progression of the bass a fourth Its connection 

, , with various 

upwards or a fifth downwards has been adopted. The following example will other chords, 
serve to show that the chords of seventh with augmented fifth may also be 
with connected with other chords of various degrees and in different keys. 



170. 



m 



~izr 



^^sE13 



5 



jf^-Era 



U?-j Di g 

>i? 3 — IE 



fe: 



^EEH 



^ 



S 



E^E 



5 — 

4 S 

6 9 8 



4 
sir 



etc. 



±E 



-ftg- 



Z2ZZZZZ2: 



=§^= 



C: V' 7 a :V. C : Y' 7 d : vu° i. C : V 7 g: vn° 7 I. C: ni. I' 7 G: vn°V 7 



Many of the above combinations and progressions have been introduced in this 
work merely to show that they are possible; the student is, however, strongly 
recommended to abstain from employing them until he is thoroughly acquainted 
the simpler and more important forms of harmonic progression. 

Exercises. 



ni. Hi 



6 Fig 6 53 3 6 



:?=£ 



He 



e e 

B S 6 



?Z 



?Z^ 



2=<-. 



zz 



T*i-<3- 



m 



6ft 6 6ft 6 2 



6 
4 7 



3. 



1 6 
4 — 
3 2—6 



6 
4 7 



rcsrc^ 



^ 



3= 



^ 



?2= 



& 



Z± 



=?=Z 



2=£ 



B Rtp 



7 



2Z 



4. 
6 



6z 



6 



7 6 
3 6ft 6 — 



1221 



?3 



3 6ft 6 



-^- 



6 



^ 



^Ep 



zartzi 



In the fifth bar of Ex. No. 4 the fifth of the minor chord on the second degree is chromatically 
augmented. The effect of this combination is in its present position not unpleasant. It 
will be seen from this that the natural progression of parts will often give rise to new com- 
binations, which, however, are not of sufficient harmonic importance to require separate 
consideration^ 



70 



CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 



Chord of the 

augmented 

sixth. 



Its derivation. 



The chord shown in Ex. 161 at e (known as the doubly-diminished chord) 
gives by means of inversion a chord which is very frequently used, called the 
chord of the augmented (sometimes termed superfluous) sixth. 

The fundamental chord of which this is the first inversion, is the chord on the 
fourth degree of the minor scale, with the root chromatically raised. 



172 



P 



ffg 



#m 



Its resolution. 



The third of 
the chord 
doubled. 



Its resolution (shown at J in the above example) is determined by the rule 
that all augmented intervals must ascend. This chord is, therefore, always 
resolved into the chord on the dominant ; as in Ex. 172, where the chord of 
superfluous sixth, being derived from the chord on the fourth degree of the scale 
of G minor, resolves itself into the chord of the fifth degree, D. 

In four parts the third only of this chord may be doubled. 



173. 



m 



rrS- 



=fg: 



8 



?=2" 



Other posi- 
tions of the 
doubly dimi- 
nished triad. 



The chord of augmented sixth is sometimes termed the Italian sixth. 

The other positions of the doubly diminished chord are also available. The 
second inversion (chord of 4 ) may be employed in four parts, provided the 
different parts lie at a distance from each other ; the fundamental position, how- 
ever can only appear in three parts, and is very seldom employed. 



174 



P 



-J2Z 



Bad. 



flSs^F^p^iSi 



Better. 



o o 



w 



^g- 



The augment- The chromatic alteration of one of the intervals of the chord of seventh has 

ed chord or 

sixth, fourth, already been noticed at p. 68, where the chord of seventh was found combined 

with the augmented common chord. Of the remaining secondary sevenths, only 

one is of any harmonic importance when chromatically altered. This is the 

cnord of seventh on the second degree of the minor scale, which, with the third 

chromatically raised thus — 



175. 



9 4 ft 



CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 



71 



gives the following inversions : — 



n»P 



4 



4t 
9 



Sz 



fe=2=lg-— 



;a: 



8 

Of these the second inversion (chord of 4) is most used; it is called the Its resolution, 

augmented chord of sixth, fourth, and third, and is also known as the Gei^man 
sixth. Its resolution is founded on that of the fundamental chord ; thus, as the 
chord of seventh on the second degree resolves itself into the chord of the 
dominant (see p. 52, Ex. 121), this will also be the ease with its inversions, 
whether the third be chromatically raised or not. 

Jet 



177 



P 



%e> ■ — - 

*&Tr> ; 



n n 



Z.Q. 



V. 



If the root of this chord be omitted, the already mentioned chord of augmented sixth will be Resolution of 
found, thus explaining the natural tendency of the latter chord towards the dominant, into the chord of 
which it is always resolved (see p. 70). Mxth ented 



With omission of 
the Root. 



178. 




Or transposed into G minor for the sake of comparison with Ex. 172 6. 



Fundamental With the Third 
Harmony. chromatically raised. 



179. 



I^pi 



4 Inversion. 



With omission of 
the Root. 



g: 



* 



a 



5tS3 



v. 



3SF 



To this chord may also be added the ninth of the original root, in which case The augment 
however the root itself must be omitted. the^ixth and 

This combination gives by inversion a chord known as the augmented chord fift k 
of sixth and fifth, and sometimes termed the French sixth (£), the derivation of 
which is as follows : — 



Fundamental 
Harmony. 



With the Ninth With the Root omitted, 
added. and the Third sharpened. 



180 



P 



Inversions. 
4) 



2 ft 



ES 



m 



w 



IjeePeII 



rcr 



Its derivation. 



n° 7 



The other inversions (the chords of ^ and 24 ) are very seldom used. 

The natural resolution of the augmented chord of * is again the same as that Its resolution. 
of the fundamental chord, namely into the chord of dominant. 



Causes conse- 
cutive fifths. 



72 CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 

This resolution, however, always causes consecutive fifths. 

-te- 



181. 



.jm 



w 



32: 



iJ°r j= 



How avoided. Such fifths may be avoided in three ways, viz., lstly, by an anticipated resc 
lution of the fifth (i. e., the original ninth), as in Ex. 182 at a; 2ndly, by a 
free progression of the fifth towards the third of the same chord, as at b ; and 
3rdly, by delaying the resolution of both third and fifth, whereby the chord of | is 
introduced between the augmented chord of |j and its resolution, as at c. 

J Bad. 



182. p 



^ 



Eg 



*s> 



IZ3 Z 



I 



a ■ =j 1 1 za 



U- 



!gz^ 



^^^ 



Eg 



Better. 



i 






w 



m 



4bz 



SE 



-S3— v ? s 



Eg 



E^ 



-J 



zz 



IZ2^ 



?= 



Not to be con- 
sidered a 
chord of the 
ninth. 



Although in order to form the augmented chord of the sixth and fifth the 
ninth was added to the chord of seventh on the second degree, yet this combina- 
tion cannot be considered a chord of the ninth, but has the same character of a 
suspension which always belongs to the interval of a ninth, under whatever 
circumstances it may be employed. 

From this it may be argued that the chord of ninth ought only to have been 
treated under the head of suspensions ; it was, however, necessary to mention it 
here, since it is often (though incorrectly) considered as a real fundamental 
chord, and as such must occupy its place in the list of chords. In its correct 
form as a suspension, the ninth will be more fully explained in Chapter XII. 



1§E 



Mr 



Exercises. 



e b- 



t=t 



7 



183 



-0-^2- 



&E 



?=£- 



23t 



321 



2. 



g^M-p 



4 

3 



■6 — 

7 6 6 4 6 
g 4 8 4 8 



m 



f 6 X 



Z±^ 



'£21 



m 



n 



3Z 



H 



6 4i 
48 1 



^2= 



?Z 



6 

4 

:& 



M 



?2- 



8- 
5 4 

2 3 — 



Jt=L 



4 
8 



rzz 



S 



eS 



TABLE OF CHORDS. 



73 



TABLE OF ALL THE CHORDS OF THE MAJOR OR MINOR SCALE. 
I. Fundamental Harmonies. 



a. The Common Chord, 
184. jl =^§^^ 



w 



I. The Chord of Seventh. 



I 



9 



A. THE VARIOUS KINDS OF COMMON CHORDS. 



(1) Major common chords : — 

In the Major Scale. 



P 



-Wr- 



C: I. IV. V. 



In the Minor Scale. 



I 



w 



a: V. 



VI. 



(2) Minor chords : — 

In the Major Scale. 




C : ii. in. vi. 



In the Minor Scale. 



P 



-&=m-~ 



1 



a: i. 



IV. 



(3) Diminished chords : 

In the Major Scale. 



C: vii° 



In the Minor Scale. 



i 



V 



a : n u . vn" 



(4) The augmented chord of the minor scale : — 



1 



$=¥ 



iir. 



Inversions op the Common Chord. 



1. Chord of the Sixth. 



I 



2. Chord of the Sixth and Fourth 

r. 6 

m — g — 



9 



-&- 



74 



CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES. 



B. THE VARIOUS CHORDS OF THE SEVENTH. 



(a) The chord of dominant seventh. 
In the Major Scale. 



P 



In the Minor Scale. 



1o 



(J) The secondary seventh. 

(1) Major chords with major sevenths. 

In the Major Scale. 



P 



g 



S 



C: I 7 IV 7 

(2) Minor chords with minor sevenths. 
In the Major Scale. 



¥ 



C: li 7 



In the Minor Scale. 



i 



^ 



=SH 



a: 



VI T 



In the Minor Scale. 



i 



w 



s 



# 



a : 



iv 7 



(3). Diminished chords with minor sevenths. 

In the Major Scale. In the Minsr Scale. 



I 



w 



C: 



P 



n° 7 



(4) The chord of diminished seventh. 

In the Minor Scale. 



P 



:s ; 



(5) The augmented chord with major seventh. 

In the Minor Scale. 



I 



¥ 



Ill 7 
Inveesions of the Chord of the Seventh. 



Chord of the Sixth 
and Fifth. 



Chord of the Sixth, Fourth, Chord of the Sixth, Fourth, 



and Third. 



P 



and Second. 6 



^r 



^ 



3*= 



^ 



rc2i 



TABLE OF CHORDS. 



76 



II. — Chromatically Altered Chords. 
(a) The augmented common chord formed from the major chord. 



F3j 



C: I. 



IV. 



(b) The chord of augmented (or superfluous) sixth (Italian sixth), formed in 
two ways. 

lstly. From the minor chord on the fourth degree of the minor scale, 
with chromatically raised root (also known as the doubly diminished common 
chord). 

8 



i 



^=£ 



g: r?. 



w 






£J. 



2ndly. From the chord of seventh on the second degree of the minor 
scale (see the two following chords). 

(c) The augmented chord of sixth, fourth, and third (German sixth). 

(d) The augmented chord of sixth and fifth (French sixth), both formed from 
the chord of seventh on the second degree of the minor scale. 



With the Third 
raised. 



i 



w 



m 



^ESS, 



Second 
Inversion. 



With omission of With the Ninth added, 
the Root. and the Root omitted. 



-%*- 
Hk 



i* 



m 



n° 7 



3 , 8 
Augmented i 



Augmented $ 



Augmented ■ 



( 76 ) 



CHAPTEE XI. 



OF MODULATION. 



Modulation. 



Modulations 
described. 



By modulation is understood the transition from one key to another. Our next 
exercise will be to seek out and correctly recognise the modulations as they occur 
in the examples given ; in a later chapter we shall treat of the means by which 
modulations are effected. 

A modulation takes place whenever a chord appears which is foreign to the 
key in which the composition is commenced. The original key is then entirely 
abandoned, and all the succeeding chords must be considered as belonging to the 
new key, until another foreign chord is introduced, which will naturally cause a 
new modulation. 



The chorda 
most used in 
modulation. 



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In the above example a chord appears in the third bar which cannot possibly 
belong to the scale of C, in which key the example commences, but which is easily 
recognised as the diminished seventh on the seventh degree of the scale of 
D minor. It therefore indicates a modulation into the key of D minor, in which 
key the phrase will remain until the appearance of another foreign chord. This 
takes place in the fourth bar, where we find the first inversion of the major chord 
of 0. It is evident that this chord does not belong to the scale of D minor, therefore 
a new modulation is indicated, but whether the key changes to G or to is un- 
certain, as the chord in question may belong to either of those keys. It is, 
however, most probable that it belongs in this case to the key of G major, since 
this modulation is confirmed by the succeeding chord, which is the chord of 
seventh on the seventh degree of that key. The concluding modulation to 
A minor in the 'fifth bar is unmistakeable. 

The most important chords for purposes of modulation are the chord of 
dominant seventh and the chord of diminished seventh. All other chords are 



MODULATION. 



77 



ambiguous, and may belong to two or more scales at the same time, as was the 

case with the chord of sixth in the fourth bar of Ex. 185. 

This ambiguity often renders it necessary to examine not only the modulating Ambiguity of 
chord itself, blit several of the harmonies by which it is followed, before the new ° 01 
key can be distinctly recognised. Very decided modulations can only be effected 
by means of the chord of dominant seventh or its inversions (see Chapter XIII). 

Wherever a modulation occcurs in the following exercises the new key is to indication of 
be indicated by the ehange of the letter under the bass note (a. capital letter ^^examples 1 
signifying major and a small letter minor keys, as heretofore). The succeeding 
chords must then be considered as having then - foundation on the various 
degrees of the new scale, until another modulation takes place. 



Exercises. 



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( 78 ) 



CHAPTER XII. 

OF SUSPENSIONS. 

The simultaneous progression of all the parts of a chord, especially when, as in 
the foregoing examples, there is no variety of rhythm, occasions a certain mono- 
tony and sameness. Sometimes, however, instead of all the voices proceeding at 
the same time from one chord to the next following, one or more of the parts will 
remain stationary, while the remainder proceed to their respective positions in the 
succeeding chord. The most important of this class of progressions is termed 
the suspension. A suspension occurs when a certain expected or even necessary 
progression is delayed, in such a manner that a part which should descend one 
degree in order to take up its position in the succeeding chord remains stationary, 
while the other voices proceed independently of it. The delayed or suspended 
part proceeds to occupy its proper position later in the bar. Thus, in the 
following example — 



187. 



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Suspensions, the soprano may remain on C, while the other parts proceed to the chord of Gr 
in the second bar ; the suspended part being then resolved into its proper note B 
in the second half of the bar : — 



188. 




SUSPENSIONS. 



79 



In the same manner a suspension can be formed from Ex. 187 by delaying 

the tenor : — 



Definition of 
the terra. 



189. 



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The suspension generally forms a dissonance with the chord in which it 
appears; that this is, however, not always the case is shown by Ex. 189, in which 
the suspended note forms a chord of sixth on the bass note G. In this case the 
unusual appearance of the minor chord of the third degree between the chords 
of the first and fifth degrees, as well as its peculiar position, together with the 
delayed progression of the tenor, all combine to give the phrase the character of 
the suspension. 

A suspension may be formed by delaying the progression of any voice which 
would naturally descend one degree, provided the note which forms the suspension 
be prepared. 

The suspension in its complete form may therefore be divided into three 
subjects for consideration, viz., the preparation, the suspension itself, and the reso- 
lution or progression thereof. 

The preparation of a suspension is precisely similar to that of any other 
dissonance ; it may be effected by means of any one of the parts of a common 
chord, and also (though more rarely) by means of a seventh, generally the domi- 
nant seventh. 

Preparation by means of the Octave of the Root. 



The suspen- 
sion forms a 
dissonance. 



Suspensions 
in different 



Preparation 
of a suspen- 



190. 






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By means of the Third. 

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By means of the Fifth. 



0:1. n. vi. I. G:V. VI. 

By means of the Dominant Seventh. 



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The preparation must take place on the unaccented part of the bar (arsis), the 
suspension itself appearing on the accented part (thesis). The rule given on 
p. 50 for the preparation of a dissonance will also apply to the suspension, viz., 
*hat the preparation must be of at least equal duration with the note prepared. 



80 



SUSPENSIONS. 



The suspension itself must enter on the accented part of the bar, and may 



Entrance of 
the suspen- 
sion appear m any voice, and proceed to any interval of a common chord, or (though 

very seldom) to the interval of a seventh. 

Suspension proceeding to the Octave of the Root. 



191. 



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Suspension proceeding to the Fifth (only admissible in certain positions) 
a. " * I i b. c. d. 




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Addition of a 
seventh to 
the suspen- 
sion. 

Suspension of 
the seventh. 



The remarks on Ex. 189 (see p. 79) will apply to all suspensions proceeding 
to the fifth. Thus in the above example the progressions a and c will have the 
entire character and effect of suspensions, while that shown at d, having no dis- 
sonant effect, cannot be considered as one. If a seventh be added to the chord 
into which the suspension is resolved, as at b in the above example, the dissonance 
of the suspension will immediately become perceptible. 

The reason why the seventh can seldom be suspended, is that the suspension 
would, in most cases, form a perfect octave, and as such would not have that 
dissonant character which is essential to a suspension. If, however, the octave 
be diminished instead of perfect, a suspension of the seventh is possible, as at b 
in the following example : — 



192. 



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SUSPENSIONS. 



81 



The progression a in the above example is termed a passing seventh, of which 
more hereafter. 

The suspension is resolved, as has already been observed, by descending one .Resolution of 
degree. a aus P ension - 

(Exceptional resolutions will be treated later.) 

The note into which a suspension is resolved (i. e. the note which has been Tne »"si«nd- 

. , . , ed note not to 

suspended or delayed) must not appear in any other voice at the same time, be doubled. 

except in the bass. 



193. 



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b. Better. 



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In Ex. a the tenor proceeds from A to C, which latter note is contained in the 
suspension in the soprano ; in Ex. c the tenor takes the note G, which is already 
suspended in the alto. Both these cases are faulty, especially because the third 
and fifth of the chord are doubled. The effect of doubling the root, as in Ex. d, 
is, however, better, particularly when the natural progression of parts requires 
it, as in the following example : — 



194. 



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It may be here observed, that when the root is doubled it should always be at Suspension of 
a distance of at least an octave from the suspended note, and that doubling in the 
unison is to be avoided. 



195. 



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Between bass and tenor, however, such a progression as the above may be 
possible. 

Other intervals besides the root may, however, be doubled in the bass during 



82 



SUSPENSIONS. 



a suspension, provided the interval so doubled be introduced by a good progres 

sion of parts, for example : — 

i , bad. 

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196. 



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Consecutive The fault contained in the last of the above examples will be readily seen if 

bidden by tbe the suspension be omitted, in which case consecutive octaves will be found 
suspension. between soprano and bass : — 



197. 



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Hence it will be seen that suspensions do not interfere with the rules against 
consecutive fifths and octaves : — 



198. 



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the bass. 



Nevertheless, consecutive fifths hidden by suspensions are not unconditional! 
forbidden. 
Suspension in The suspension in the bass, which usually occurs before the third of the 
chord (or, which is the same thing, before the chord of 6 or jj) does not allow the 
note suspended to appear in any other voice. 

Bad. 

I XT -&>- -&- -<s»- * K _ 

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Suspensions of the root and fifth are seldom employed in the bass 

Bad. ^ — ^ 



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SUSPENSIONS. 



83 



The method of figuring the suspension has already been partly shown in the Figuring of 

r . n the suspen- 

toregoing examples. s i on . r 

When the suspension is contained in one of the three upper parts, the interval 
found between the suspension and the bass is indicated, together with its resolu- 
tion ; for example : — 

4 3, 9 8, 7 6. 

Where necessary, other figures are added to indicate the chord into which 
the suspension is resolved, thus : — 

9 8 6 - 7 6 
6 -, 5 4, 4 -. 

When the suspension lies in the bass, the accidental intervals occurring 

5 _ 5- 
between the bass and the upper voices are indicated, for example : — 2 _ or 4 - 

the horizontal hues in each case signifying that the accompanying voices remain 
stationary during the resolution of the suspension. 

iL suspension in the bass is also sometimes indicated by an oblique fine over 
the suspending note, the ordinary figuring of the chord into which the suspension 
is resolved being then placed over the succeeding note ; for example : — 



201. < 



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Exercises. 



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Vocal clefs. 



The C clef- 
its relation to 
the other 
clefs. 



In accompanying the above exercises it will be advisable to write each voice 
on a separate line or stave, both in order to obtain a clearer view of the progres- 
sion of every single part, and also as a useful preparatory exercise in reading 
from score. 

Inasmuch as the four different voices are always considered as vocal parts, it 
will also be better to write each part in that clef which originally belonged to it, 
instead of employing the violin clef as heretofore. 

The clef which is used for the three upper vocal parts, viz., the soprano, alto, 

and tenor, is called the C clef, o o J 

For the lowest vocal part, the bass, the F — clef (§j is employed. 

In order to show the relationship of the C clef to the violin and bass clefs, we 
will make use of a large stave of eleven lines. Such a stave will be formed of the 
two smaller staves already employed for the violin and bass clefs, together with 

an intermediate line, on which is placed the C clef fen, which thus occupies the 
position of the first ledger line above the bass or below the treble staves, 
namely, 0. 

FGABCDE FOAB DBF Q ABODEFG 



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Of these lines the lowest five are used for the bass or lowest voice, while for 






SUSPENSIONS. 



85 



the three other voices different staves are selected, each consisting of fiv, lines, as Selection o.' 

c 11 small staves 

follows :— for the dif . 

ferent voices. 
Bass. Tenor. Alto. ooprano. Violin. 



204. 



m 



Hence it will be seen that in consequence of different staves of five lines each 
having been selected from the large stave for the soprano, alto, and tenor voices, 
the C clef will necessarily occupy different positions in the various staves ; that 
is to say, in the tenor stave it will be found on the fourth line, in the alto stave 
on the third line, whde in the soprano stave its place wdl be on the first line. 

In all these cases it will, however, be the same C, viz., the C on the first 



Position of 
the C clef in 
the various 
staves. 



ledger line above the bass stave Sjz 



The relative positions of the same notes, written in different clefs, will be best 
shown by the following example : — 



205. 

Violin Clef 



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The accompaniment of the exercises given in p. 83, will require a somewhat 
free treatment of the voices with respect to their progression, since in order to 
obtain a good position of the suspensions it will often be necessary to alter the 
form of the chords, and to employ the extended position alternately with the 
close. 

In altering the position of the voices the following rules must be observed : — 

A simultaneous change of position on the part of all the voices is not allow- 
able, except in certain cases, when they proceed to different inversions of one and 
the same chord. 

Each voice may abandon its position at any time, provided one or more parts 
of the chord remain stationary. 



Variety in 
the position 
of voices. 



86 



SUSPENSIONS. 



The following accompaniment of Ex. 8, p. 84, will show the application of 
the above rules : — 



206. \ 



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Description of 
Ex. 206. 



The close position in which the above example commences is abandoned in 
the fifth bar, and the extended position is adopted, and employed until the 
eleventh bar, when this is again exchanged for the close position, in which the 
phrase concludes. 

This variety of position is effected in the first place by a free progression of 
the soprano, which iu the fifth bar springs from its natural position into the 
dominant seventh E \>, a leap which is perfectly allowable when, as in the present 
case, the root of the seventh is already present in the preceding chord (see p. 50). 

Again, in the seventh bar, the soprano abandons its position and leaps into the 
fifth, G, the other voices remaining stationary, by which means the suspension 
appears in a better position. Finally, the close position is again attained at the 
end of the tenth bar by means of a free progression of the tenor. 

Although, on account of its occupying less space, we shall continue to employ 
the violin clef for our examples, the student is strongly recommended to write all 



RETARDATIONS. 



87 



future exercises in score and with the four vocal clefs, in the manner shown in 
Ex. 206, since an intimate acquaintance with the various clefs is absolutely 
indispensable to every musician. 



OF RETARDATIONS. 



A retardation is said to occur when the upward progression of a voice is Retardations, 
retarded or delayed, in the same manner that a suspension delays its downward 
progression. 

Most progressions of this kind are caused by a shortening or contraction of an Their general 
ordinary suspension followed by an upward progression, for example : — 



207 



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Formed from 



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Keal retardations may however be formed by delaying the progression of the Real letard*. 



leading-note : 



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208. 



'T T 



and also of many other intervals which should have an upward progression -rf 
a semitone, especially in tbe case of those chromatically altered chords which 
contain augmented intervals. 



209. 



U^^B^JbS^, 




Observe, that as in the case of the suspension, the note into which the The retarded 



retardation is resolved must not be contained in any other voice except the bass. 

The last of the above examples gives us the combination which has already 
been found as a chord of seventh on the first degree of the minor scale (see 
page 44), and which (as was stated on page 45) is unavailable in its fundamental 
form. It is however evident that as it appears in the above example, it is not to 
be considered as a fundamental harmony, but merely as a retardation of the 
leading-note. 



note not to be 
doubled. 



te8 



SUSPENSIONS. 



Double sua- Suspensions may appear in two or more parts at the same time : — 

pensions. 



In two parts. 



210. 



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In three parts. 

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The chord of 4 often appears as a double suspension : — 




Hitherto only two chords have been employed for the preparation, entrance, 

The progression of parts will however often 



Resolution of 
the suspen- 
sion by means and resolution of the suspension 

chords become richer and obtain more variety if three chords are introduced. 

How effected. 



This is effected by allowing one of the voices (generally the bass), or even several 
at the same time, to proceed to a new harmony at the same moment that the 
suspension is resolved. The note into which the suspension proceeds will always 
form one of the component parts of such new harmony, for example : — 

By progression of the bass : — 



212. 



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By progression of several voices : — 



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-^s — n 



Chords of the j n illustration of the views advanced in Chapter IX. on the subiect of chords 

ninth treated r * 

as suspensions of the ninth, it may here be observed, that many cases in which the ninth occurs, 
means of and which would be recognized and treated by many theorists as chords of the 

three chords. 



SUSPENSIONS. 



89 



ninth, may be much more simply explained by considering them as suspensions 
accompanied by three chords, thus : — 



Suspension of the Ninth, 
with two Chords. 



214. p 



-A 



Suspension of the Ninth, 
with three Chords. 




In like manner four chords may also be employed for the preparation and Suspensions 
, . j. . . , , , . , . . , . . , , resolved by 

resolution or a suspension, provided the note into which the suspension is resolved means of foui 

is not contained in any other voice. ° ° 



215, 



I 



W 



2 3 



Without the Suspension. 



:SE 



2=s- 



st 



^2: 



1- 



5 
4 



^E 



*~^%- 



=& 



TV. n. vn° 



VI. 



Exercises. 



1. 8 — 

8 7 



e 

4 7 



216. 13L 



S3 



:£=" 



■&- 



ZZ2I 



-P2=-0- 



-P3I 



~T}- 



2. 



j=E5ij Ff7 ^E^ 



7 6 
6 



3 



aa 



^ r= > 



6 

7 4 



^ 



ehe 



1=2- 



'ciz 



m 



6 7 — 
4 — 8 



3. 



C=i= 



3B 



2± 



:c± 



-E^-lfe 



:J=F 



ai 



r, 

4 
8 



6 
4 7 



7 « 



rt 



nzL 



4t 
a 



6 7tj 



^= 



2± 



z±: 



E 



5t3t 



*E 



^2: 



-P2= 



E 



Between the suspension and its resolution may sometimes be found notes 
introduced for the sake of varying the melody. 



Notes intro- 
duced be- 
tween the 
suspension 
and its reso- 
lution. 



90 ANTICIPATIONS. 

These notes may be either notes belonging to the harmony, for example : — 

* * * 

_#! I- : - I I I rs , J I J 



217. 



S 



S 



U^g: 



~es~ 



or notes foreign to the harmony, for example :— 



3± 



rz>-r* 



I *, 



L^as 



3± 



218. 



._C2 ~22! 



Z2I 



T X 



32; 



"C - 



The above and similar melodic progressions will be explained in the chapter on 

passing notes. 

Suspensions Cases may also be met with in which the suspension has no resolution 

without reso- 
lution, whatever. 



219. 



-?=?&- 



=± 



Or more frequently. 



z^s 



^P-S^-z^. 



3t3t 



r 



Such phrases are formed by the omission of one or more notes of the following oi 
some similar phrase : — 



220. 



"2=; 



^L£ 



Or, 



±± 






? 



321 



"22* 



J-l— I— J- 



-E2" 



Anticipa- 
tions. 



When em- 
ployed. 



OF ANTICIPATIONS. 



The anticipation of a note, which is not so frequently employed as the suspen- 
sion, occurs when one or more voices proceed to notes of the following chord 
before they are required to do so by the rhythmical formation of the phrase. 

Progressions of this kind are seldom employed in slow tempo, or with long 



notes. 



221. 



Anticipation in the Bass. 



In the Soprano. 



3=fc 



T2&- 



d=^H=^ 



r r 






EZi^: 



S=xst 



In several voices. 

1 ' -K- 



3^ 



Hfe 



I 



ANTICIPATIONS. 



91 




The note which forms the anticipation need not always be exactly the one Other notes 
which is expected on the appearance of the second chord. A different note, if it harmony used 
belongs to the harmony of the second chord, may also be employed as an antici- *f ^ tlclI>a ~ 
pation, as in the following much-used cadence : — 



222. 



P 



=gt 



Or, 



y=^J, 



& 



: S : 



Another kind of rhythmic variety occurs when one voice does not proceed to Rhythmic 
its place in a chord until after all the other voices have taken up their respective one a v i^° n 
positions. Such progressions resemble suspensions, inasmuch as both preparation 
and resolution take place, but differ from them in the important particular, that 
they are formed by rhythmic rather than harmonic variations, and cannot appear 
singly, but in sequences such as the following : — 



223. Allegro. 




With such progressions must also be classed the unisono passage in the 
" Leonora " overture (No. 3) by Beethoven. 



224. 



^=3 



4^32 



2 



m^ 



N^^^ 



-'-J-'lj- -zd- — -"S-fl**- -id-^;**--*'- -e* 




2=P — =£ 



92 




W- W 



5 — F— g J r I ^ 



ANTICIPATIONS. 



= F=^=F 



it 



^=t=M^fe 



-F- f t=f— 



T r 

^ fe=2 



3<~ 



■ifr i 



FT 



I 



fc*-^v -g- k 



; p 



3fe 



£^ 



s 



( 93 ) 



CHAPTER XIII. 



OF THE MEANS OF MODULATION. 



The meaning of the term modulation has already been explained in Chapter XI. 
We have now to treat of the best means of effecting modulations. 

The art of modulation consists in finding those harmonies which are related to 
two or more scales or keys, in order by their aid to proceed satisfactorily from one 
key to another. 

Modulations may be of two kinds, and have two different objects in view. 

Firstly — They may appear abruptly, and the new key may pass away 
quickly, or 

Secondly — They may be more gradually prepared, in which case the new scale 
will serve for some time as the foundation of the harmonies employed. 

In the first case the modulation will be introduced by the simplest and 
quickest means, and although it may be distinct and unmistakeable, the new key 
will soon be abandoned and a fresh modulation introduced. In the second case 
the modulation will generally be gradually prepared by various means, and the 
new key will remain long enough to become familiar to the ear, and may even 
lead to a perfect close. 

Thus in the following example, the modulations are transitory, and the key 
changes rapidly without wandering far from the original key of C major : — 



The object of 
modulation. 



Transitory 

linn lu hit i j ns. 

Gradual and 

permanent 

modulations 



225, 






r 



3»=J 



4i- 

2 



£ 



^ 



C: I. F:V 7 L IV. G:V 7 I. IV.a:V 7 I. rv. C:I. V 



This kind of modulation is most suitable for the more nearly related keys. 

In the next example the more distant key of El? is sought by degrees, and 
when it is reached the original key is entirely abandoned. It will be seen how 



94 



THE MEANS OF MODULATION. 



the transitory modulations are employed as means of introducing the final 
modulation into E|?, which is the object of the phrase : — 



226. 



E 



F 



-p<& 



=^ 



ffi 



--m-- 



7b 
6" 



T 1 



±at 



T 



5 



a^ 



H 1- 



rct, 



:fe 



j§i 



I. bt>: vu° 7 bFTi. VI. f:V 7 



Ef: V 7 I. 



i*: 



V. 



The means of 
modulation. 



Employment 
of the chords 
of tonic and 
dominant of 
the new key. 



In considering the means by which modulations are effected it will not be 
necessary to distinguish between the above two different lands of modulation, 
since the same means will serve for both. 

The first and most simple means of modulation will be the chord of the tonic 
of the new key itself. 

If this chord is identical with one of the chords of the original scale, it will 
only require the dominant harmony of the new key to make the modulation com- 
plete. Thus, in the following example, the chord of G, being already one of the 
chords of the scale of 0, requires no connecting link with the original scale ; the 
modulation will however not be perceptible until the third fundamental harmony 
of the new key be heard (namely, the chord of the dominant), as shown at b : — 



227. 



V 












■ffc ^ — 


<s> 


fj 


S> 




<& 


4B <g 1 


&> 


<s 


s» 


*« 


o 






-s-- 



_2zr 



The effect in modulation of the minor chord of the tonic is certainly more 
decided, but even this chord requires the chord of dominant of the new key to 
render the modulation unmistakeable. 



228 



w 



I 



m 



* 



^ 



e 

5b 



~-X2~ 



3iE 



~?7 3- 



ZE2Z 



e: i. 



C: L 



f: i. 



51= 



The major chord of the new key, when not followed by its dominant harmony, 
has itself somewhat of the effect of a dominant chord : — 



229. 



P 



^ 



m 



~CS7 



a: V. 



m 



~Z2Z 



ZC2Z 



C: I. 



=#=* 



3f^ 



'.: V 



_c^ 



THE MEANS OF MODULATION. 



95 



The chord of the tonic is seldom employed in modulation in its fundamental Employment 

1 " of the chord 

form, since one of its inversions, the chord of 4 > has the property of rendering the of 6_ 
modulation much more decided than the root chord. In this case also the chord 
of the tonic is followed by that of the dominant, which completes the modulation. 



230. 



ii 



¥ 



m§t 



-JZE. 



m 



■3=£_ 



a 



=± 



-2: 






^-^J^r-4 



g^s= g=i=gr-* 



- f 5 — ^ 



:czrri 



v r - r 



I. G:I. V. I. C:I. a:u°. i. V. 



3Zzd 



-dr 



=e± 



C:I. V. d:i. V. 



If this chord be employed on the unaccented part of the bar, the modulation On the unac 
... cented part of 

•will not be so decided. the bar. 



231. 




f^i- 



3=t 



IS 7 

7fr 






^k 



ZQT 



^z= 



6 



A still more effectual means of modidation is the chord of the dominant, and 
especially the dominant seventh, which renders the new key clear and unmistake- 
able. 

According to the principle that the connection of chords one with another 
is best effected by means of notes belonging to two successive chords, and 
remaining in the same voice, modulations may be formed through the chord of 
dominant seventh from the chord of the tonic of the original key to any other key 
excepting those of the minor and major thirds and the augmented fourth. Thus 
from the key of into all keys except E|?, E, and F$, modulations may be formed 
as follows, the connection being in each case observed by means of notes which 
remain stationaiy, and indicated by means of binds : — 



Employment 
of the domi- 
nant seventh. 



Modulations 
by means of 
the dominant 
seventh into 
nearly all 
keys. 



C to F. 



C toG. 



C to a. 



232. 




In order to modulate into the remaining three keys, E|?, E, and 



it, , Modulation 

J, another ulto the re- 
maining keys. 



96 



THE MEANS OF MODULATION. 



chord will be required (generally a common chord) which will supply the desired 
connection, for example : — 

From C to E b- 



CtoE. 



C to Ffl. 



233. jfel^ilfel 



minor simi- 
larly effected. 



ESF = 13 ::=:: ^ =:r S= 



7ZJ U 1 ^- c^— 



ISlSfes 



^r 






Modulations Similar modulations may be formed from the minor, as follows : — 

from the 



From a to b. 



a to d. 



a to e. 



234. 




^^ 



33FgfeE 



a to F. 



-e— 
a to G. 



~22T 



-£5 r -, 'S' ^. gj- 

a to B b. 



~Z3~ 



2Z 22T 



«<=3 *«=3 C-*' U ,«— a _ __ U »*=3 bc-i,=3 1 



' = ^^=w 1 



By means of additional chords, modulations may be formed from A minor to 
the remaining keys as follows : — 

a to D b. 



From a to C. 



235. jE^^. ^ g: 



g 






Eft ks 



a toEb. 



a to F $. 



a to A p. 



^=&^gE&E3E^^&£&& 



— >-j— S-iS- 




The connec- It is of course understood that the above examples merely show the principle of 

tion of modu- modulation, and that it is not necessary for modulations always to be effected in the 

latmg chords ' ^ 

not always manner there shown. Nor is the above-mentioned connection of chords always 
requisite, as will be seen by the following example : — 



necessary. 



Employment 
of the dimi- 
nished 
■eventh. 



236. 



I 



C to E 17. 



C to e. 



a to C. 



-7 



^^i^Eg^^3&^^p 



3£ 



-£?• 



The student is here recommended to write out modulations from and to all 
keys, major and minor, and in so doing to employ all the various positions of the 
chords. 

Another equally important chord with the dominant seventh is the chord of 
diminished seventh, which is often more peculiarly suited for purposes of modulation 



THE MEANS OF MODULATION. 



97 



than the former, especially in those cases in which the seventh and root of the 
dominant harmony would be obliged to enter without preparation. 

The following examples will show the application of this chord to modulation: — 
C to Bb. C to B. C to d. a to o. 

etc. 



237. 




This chord also possesses peculiar capabilities for modulation, on account of its Enharmonic 

modulation. 
e?iharmonic qualities. 

The following chord, being written with a different notation, will belong to 

four different keys, although the sound will in each case be the same : — 



238. 



\=$$%=E§ 



m^M 



3 s — Y^n 



In the first of the above cases, the chord belongs to F minor, in the second to 
D minor, in the third to B minor, and in the fourth to A (7 minor. 
Thus, by means of one chord, four modulations are possible : — 



239 



i 



¥ 



C tof. 



Ctod. 



Ctob. 



"feT" fcs 



a:=flg3:=g— H =g? — fg — ~i & — 



ifcrg. 



~W 



C to at>. 



^m 



"sfww 



To these may be added four more modulations into the major keys of the 
same names as the above (for the diminished seventh is often used instead of the 
seventh on the leading note of the major scale), thus giving eight modulations by 
means of one chord. The modulation into major by the diminished seventh is 
shown in the following example : — 

C to D. C to B. 



240, 



i 



w 



1 



£=fe 



-rs ITS- 



fe 



etc. 



If now we consider the final chord of the above example as a chord of domi- 
nant instead of a chord of tonic, new modulations become possible, and such 
modulations will be rendered still more decided by the introduction of a chord of 
4 (derived from the new tonic) between the diminished seventh and its resolution, 
in the manner shown on page 61, for example : — 

C to G. c to e. 



241. 



t=s== 






Jg=rg=fl= 



ZZ2.Z. 



m=m^^^ 



I s 



pppp 



■z? 



98 



THE MEANS OF MODULATION. 



Enharmonic 
alteration of a 
chord. 



Progressions similar to the above may be formed from each of the four posi 
tions of the diminished seventh shown in Ex. 238 ; and as in each case the modu- 
lation may be either to a major or a minor key, it follows that there are eight 
more modulations possible by means of the same chord of diminished seventh, 
making a total of sixteen modulations, of which eight are into major, and eight 
into minor keys. 

It will be observed that the alteration of the notation necessarily changes the 
intervals, though not the sound, of the chord; the different notations will therefore 
be in reality inversions of the chord, for example : — 



P 



h 



242 -^g^^*^te 



c«° 7 



afl° 



S7 



Enharmonic 
modulation 
by means of 
the augment- 
ed chord of ~ 
5. 



A similar capability of enharmonic change is possessed, though not to so great 
an extent, by the augmented chord of 5 . The resemblance which the sound of this 
chord bears to that of the dominant seventh permits the one chord to be 
substituted for the other, and thus certain modulations may be effected, for 
example : — 



c tob. 



243. 







PEf 



1^^- 

m 






£ 



E \> to d 






-A 



I. 



b:n°, 



V. 



I. 



Ei?:V 7 d:n°, 



V. 



Exercises in 
modulation. 



Hitherto we have considered the means of modulating quickly from one key to 
another. Since, however, it is not always an object to modulate as quickly and 
distinctly as possible, the following will be a very useful exercise : — 

To modulate from one key to another by means of the common chords of the 
different degrees ; for example : from to D through the common chord — 



Of the Third Degree. 



244. 



ZJCZl 



# 



:c3i 



Of the Fourth Degree. 



Eg^Sl 



Of the Fifth Degree. 



Of the Sixth Degree. 



Of the Seventh Degree. 



EXTENSION OF MODULATION. 



99 



/rom to E through the common chord : 



Of the Second Degree. 



Of the Fourth Degree. 



245 



•P 



321 



32 _ 
T£2T 



Of the Fifth Degree. 



fczi 



fc 



=S- 



Of the Sixth Degree. 



Of the Seventh Degree. 




^=#teF 



Z22C 



ESE 



f 



^ 



-#P*3 



The above examples will he sufficient to indicate the manner in which othe? 
modulations may he formed according to the same principles. 



OF THE EXTENSION OF THE MODULATION, AND OF ITS COMPLETION 
BY MEANS OF THE CADENCE. 

In order to form a longer and more gradual modulation than any that have 
hitherto been met with, the same means will be employed, but not in so direct a 
manner. That is to say, instead of proceeding to the new key by the shortest 
and most direct means, transitory modulations will be employed, and the new key in- 
troduced by degrees, and when reached, will be as it were fixed and rendered distinct 
by means of the cadence. 

Thus, in the following example,' the modulation from C major to E minor 
takes place through D minor, A minor, and G major, and is completed by a 
cadence in E minor : — 



Gradual and 

permanent 

modulations. 



The modula- 
tion com- 
pleted by tha 
cadence. 



246 



tUt 



SESEl: 



z± 



^rF=W^ t 



^t^S^a 



^Fi^fS 



1^- f-fe 



g 



>7-f- 



m^m 



^ 



2P7 



C : I. d : vn° 7 i. a : vn° 7 rv. 



i. G:V 7 I. e:V, 



V. i. 



If the modulation be effected by means of the chord of 4 derived from the The simplest 
tonic chord of the new key (see page 95), such chord of 4 will only require to be cadence, 
followed by the chord of dominant with its natural progression to complete the 
cadence, for example : — 



247. 




100 



1HJS MKAi\S OF MODULATION. 



The extended In other cases the extended or prepared cadences must be added to the modula- 
tion in order to confirm the new key. The following are the two simplest forms 
of the extended cadence : — 



Or in other Positions 



248. 



e£ 



SF 



c=g=<=: 






J 



wk 



M- 

"J 



-S3 



W^^g^ 



p^p 



6*7 



^): 



~w 



tg: 



6 

4 7 

3Z 



5 



:22: 



IS 



3= 



=ii£ 



^EmEE- 



Or in other Positions, 



^3 



:BE 



EEgE£)5^# 



IS=EEg^l 



35): 



feS 



J^ 



&g: 



^ 



g 



:& 



zc2: 



2± 



PI 



The position of the chords forming the cadence will be determined by that of 

the final chord of the modulation. 

Addition o£ The following examples will show the addition of the above two cadences t 

the cadence , , « , , , , ■. 

to the modu- am ' o to some or the examples already given : — 

la tion. 



249. 



Ex. 233. From C to Et>. 



Cadence a. 



c r 



3 



ciz 



ffi 



2a; 



eb 



H 



* 



m 






53: 



^ 



fb 






Ex. 232. From C to a. 



idSE 



Cadence a. 
—1 



b; 



3 



■^L If 



g 



:s2: 



:e=L 



:^= 



3ir 



^ 



~s^~ 



^t- 



:czr 



Ex. 232. From C to B. Cadence 5. 




§N# 



^^i^p^i^p.^^^ 



:|g: 







E#E 






:l^ 



EXTENSION OF MODULATION. 



101 



Ex. 232. From C to D \f. Cadence h. 



:^^j^^^fe=g=^ 



& ib r & 2 =^ 



£=t 



^ 



--&=L 



The following is an example of a modulation from Q major to A\> major, by 
means of transitory modulations through E minor, C major, and B|? minor. 



250. 



gfc-r 



n 



g u t^k nd 



Cadence. 



JN 



^E5fc£ 



km 



l^fy&<^g-B 



&^i 






232Z 



P liP'TiF 



£ 



e 



3± 



*i§£ 



^m 



--i^r- 



m 



1 



103 



HAEMONIC ACCOMPANIMENT TO A GIVEN VOICi; 



CHAPTER XIV. 

OF THE HARMONIC ACCOMPANIMENT TO A GIVEN VOICE 

(CANTUS FIRMUS). 

In treating of the harmonic accompaniment to a given voice we shall consider the 
simple melodic 2)rogression of each part, and all other elements of a melody, such 
as metrical and rhythmical variations, will remain for the present out of the 
question. 



THE HARMONIC ACCOMPANIMENT OF A GIVEN SOPRANO. 



Progression 
of baas. 



Cantn3 
firmus. 



In every harmonic phrase the progression of the bass is the most important. 
The following simple melodic phrase being given as an exercise — 



251. 



P 



~r^~ 



and the roots of the various narmonies which may serve as its accompaniment 
being indicated thus — 



252. 



P 



G 



G 



^ 



IZ2I 



we direct our attention in the first place to the progression of the bass, which 
according to the roots indicated may be as follows : — 
253. . C G C d G 

Soprano. 



Bass. 



w 



1Z2Z 



I^rS 



rzsi 



rzz 



1221 



or thus : — 



254. £E 



~tj- 



rs2i 



HARMONIC ACCOMPANIMENT TO A GIVEN SOPRANO. 



103 



The addition of the middle voices will then present no difficulty, they may Addition of 

the middle 
voices. 



proceed as in the following example, and the phrase is complete : — 

C G C d G C 

Alto 



255. 

Soprano. 



Tenor. 
Bass. 



i 


(h 


» S3 


s> 


n> 


<S — 


O 


t'j 


s 


H" 




tS 


<s 

-S>- 


.£2- 


<S> 

JZ2- 


-s>- 


fi^s- 




tn 






f-J 




i 




Al 








\J> I 


rj 










i*3 

















In order more clearly to explain the principles of a good progression both of 
the bass and middle parts we shall make use of examples indifferently accompanied. 

Exercise : — 







C 


F 


G 7 


C 


d 


G 7 


C 


. \# 










s 






256. -\ 


ttrt 




/"■j 


s> 






— s> 





















Defective accompaniment to the above : — 



257. 



P 



¥ 



-& — u 



IZ2I 



6 



~r?~ 



IZ2T 



The above example does not contain a single violation of any of the rules of 
progression, &c. hitherto advanced ; nevertheless it is meagre on account of the 
stiffness, weakness, and insecurity of the bass. 

In a good harmonic progression of the bass, no note must remain stationary 
unless it is required to do so in order to serve as the preparation of some dissonance, 
or unless it is equalized and counterbalanced by a very decided progression of all 
the other parts. 

Ex. 257 also contains in two places the chord of 4 ; this circumstance will 
afford an opportunity to speak of the employment of this very peculiar chord. 

The use of the chord of 4 depends on certain conditions. It is most frequently 
to be met with in the formation of cadences, and also in modulations. (See p. 95.) 

In both these cases it may enter without preparation, but always on the 
accented part of the bar (thesis). 

It may also appear under other circumstances — viz., when the fourth is pre 



Exampk ci 
ari incorrect 



Rule for pro- 
gression of 
the baas. 



Genera] em- 
ployment of 



the chord of 



4. 



104 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



pared, and when the bass proceeds by one degree to its place in the next following 
chord, or remains stationary, for example : — 



258. 




U=^U±±A 



s=g*=i 



s 



3S 



2^3= 



W 



r^-p- 



t=t 



?= 



zc2 



2± 



^= 



^ 



^B 



=5i r s g 



?=g; 



If used on the unaccented part of the bar (arsis), it may appear under the 
same conditions as in the above example, and, in addition, may be used with the 
bass prepared instead of the fourth, for example : — 



259. 



P 



=L 



3= 



3£ 



3 



B 

-<S>- 



a 



6 

4 



^ 



.a. 



32T 



Its effect If the chord of 4 appears on the arsis it must be considered as a passing chord, 

ferent circum- if on tne thesis it will have the character of a suspension ; its effect will however 
stances. ^ e yer y wea k {{ introduced on the thesis with the bass prepared (as was the case 

in Ex. 257) :— 



260. 



P 



=23- 



-rz)~ 



m 



ZZ±L 



-PZ- 



SE 



3=: 



6 

4 



r^= 






IC3I 



Its appear- 
ance as a sus- 
pension. 



It also frequently appears as a real suspension, in which case the preparation 
of the fourth is fully explained and justified. 



S ^^ = 



261. 



rz2i 



r t 



3=f 



:£2; 



HARMONIC ACCOMPANIMENT TO A GIVEN SOPRANO. 



105 



When all the parts proceed by single degrees, and the notes are of short It3 appear- 

r g r . & i ance without 

duration, the chord of 4 may enter without preparation. preparation. 



262. 




ESEEES 



fe^E 



_2 5 _iv 



=g= 



& 



-£2 



The chord of 4 derived from the diminished common chord is seldom used in The second 

inversion of 
four-part harmony. the diminish- 

ed common 
. -_ , chord. 

-A — 4- 



•263. 



P 



~Sz 



2± 



E3E 



^E 



In the three-part phrase, however, it may be employed, and frequently supplies 
6 
the place of the chord of 4. (See the chapter on the three-part phrase in the 

second part of this work.) 

A correct and pure harmonic progression not only requires that the bass shall 

form a clear and intelligible harmonic foundation to the phrase, but also that each 

voice shall proceed according to certain melodic rules which we shall now proceed 

to consider. 

Certain progressions have always been considered anti-melodic — for example, Anti-melodio 
i e ■ i- • progressions. 

two consecutive leaps of a fourth or a fifth m the same direction. 



264. 







rj 






— & 1 


I — & — 1 






IP). 














r J 




\,' 


















r-i 






— & — 













The above progressions may be corrected as follows : — 



















n 


265. (IS 


— <s> — 






— & — 


— 




rJ 




r-J> 




1 — o — I 


' — <s 




r-> 









Even leaps of a sixth are better avoided, and the progression altered to that of 
a third in the contrary direction. 



266. §§= 



Better. 



izsr 



_£2_ 



Better. 



~w 



106 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



Progressions Progressions of augmented intervals are anti-melodic, and as such should not 

of augmented ° nr • t ■ • i i ■ 

and diminish- be employed (see page 25) ; progressions of diminished intervals are however 

ed intervals. i, n 
allowable. 



Bad. 


>*3 


Better. 




Bad. 




D 


Better. 




9.R7. f»>: — « — 




G> 






— *" 












— & — 


rj 




r^ 


~~ 8S 


Bad. m 


Better. 




Bad. 

— o 


F+^fl 


Better. 

(S 


Jr 3 


i«i CJ. . __ 




rj 


L#J 










=|e u 



Of a major 
seventh. 



The leap of a major seventh is always to be avoided, 
Bad. Bad. 

m 

268. P ^r— 



-£2_ 



"W 



Of a minor The leap of a minor seventh is allowable in two different positions of one and 

the same chord, but not when the harmony changes. 

Not to be 

recommended. Bad. 

i3g33S 



269. 



m 



S3 



ZZ3Z 



IZ2I 



=33 



-F^o- 



^ 



231 



j£- 



e 



K 2 



7b 



~vrr 



-£=2_ 



j£. 



Rules of 
melody 



Exceptions to the above rules may often be met with ; their explanation and 
excuse will lie in the peculiar character of the composition. Nevertheless, the 
strict observance of all rules will always be very advantageous in theoretical 
studies. 

These few remarks will be found to contain the principles of a good melodic 



equally appli- progression, and will suffice for the present simple exercises. It may be observed 
cable to all that the above rules of melody do not refer to the progression of the bass alone, 
but apply in general to that of all the voices. 

The correct accompaniment of Ex. 257 will be as follows : — 



270. 



I 
1 



I 



Sf 



3BE 



-jzzi 



jzi- 



f*= 



52: 



221 



i22r 



HARMONIC ACCOMPANIMENT TO A GIVEN SOPKANO. 



107 



I 



Exercises. 



i. 



321 



271 



W 



2Z 



G. 



C. 



P 



321 



Ci_ 



G 7 



G 7 



i 



~« : 



32T 



9 



4. 



321 



G. 



G 7 



XT 



G 7 



321 



37~ 



P 



c. — 



G 7 



G. 



G 7 



S 



32Z 



P 



32; 



321 



~^~ 



6. 

Pi 



* 



Bb 



Bb 



§7 



F. 



327 



32Z 



7. 



7t-i 



£^=^ 



c. 



g7 



c. 



zz 



32_ 



F. 



321 



W 



Bb 



g7 



^E 



321 



33C 



3z: 



F. 



d. 



C 



g- 



d. 



g7 



Although the foregoing exercises are written in the violin clef, the student is 
recommended, for the sake of exercise, to transpose them into the soprano clef, 
and to write the accompanying voices on separate lines and in their respective 
clefs. 



Exercise — 



C. 



272. 



m 



a. 
321 



d 7 G 7 



C. 



7T 



Incorrect accompaniment. 



273. 



i 



HP 



-J- A 



ZZZ1 



±3 
6 
6 



& 



Exercise in- 
correctly 
accompanied. 



108 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



The faults of the above example are three in number — viz., firstly, the doubling 

of the bass of the chord of sixth in the second bar, which being the third of the 

original root should seldom be doubled ; this is however a slight fault, and one 

which can easily be corrected. A much graver error is the second in the above 

example ; this is the progression of hidden fifths between bass and soprano in the 

fourth and fifth bars. The third fault consists of the free entrance of the 

dominant seventh in the last bar but one. 

F fth e ? tra ? ce With regard to this last error, it has already been stated on page 50 that the 

nant seventh dominant seventh may only enter without preparation when the root is alreadv 
and its root. t . . .. J . , n . . , . J 

present in the preceding chord and remains in the same voice. 



274. 



sfe 



I 






33S2I 



m 



A A. 



I^T- 



=& 



2=fc 



In contrary 
motion. 



In similar 
motion. 



The free entrance of both root and seventh is less harsh in contrary motion, 
though still against the rules of harmonic connection. 



275. 



i 



w 



rs 



~^~ 



In similar motion, however, it is always to be avoided. 

276. jiiEg =i^ 



~tz>- 



sar 



Hidden fifths 
and octaves. 

Rendered 
visible. 



The second and most important fault in Ex. 273 will afford an opportunity 
of considering more fully than has yet been done, the progression of hidden 
fifths and octaves. 

Hidden fifths or octaves occur when two voices proceed in similar motion from 
any interval to a perfect fifth or octave (see page 14). 

The fifths and octaves will at once become visible if the leap taken by one or 
both of the voices be filled up by the intermediate notes, as in the following 
example : — 

Hidden Fifths. 



277. 



zzar 



rczi 



zza: 



P 



Hidden Octaves. 



zz: 



"22" 






~Z?" 



1 



HIDDEN FIFTHS AND OCTAVES BETWEEN EXTREME VOICES. 109 

Although certain hidden fifths and octaves should be avoided, yet if such pro- 
gressions were entirely excluded from the four-part phrase, the choice of chords 
would become extremely limited, and the progression of parts very much confined. 

We shall therefore proceed to make some observations on the employment of 
these progressions, although positive rules, which should be applicable to all cases, 
cannot be given. 

Hidden fifths or octaves may be caused by various kinds of progressions ; for Various kinds 
example : one voice may proceed from any one degree to the next above or below s i ns which 
it, while the other voice leaps a greater or less distance (in which case the leap {^ddenfifths 
may be either hi the upper or lower voice) ; or again, both voices may proceed by or octaves, 
leaps. 

In either case the hidden progressions may occur between the extreme voices, 
between the middle voices, or between an extreme and a middle voice. 



HIDDEN FIFTHS AND OCTAVES BETWEEN THE EXTREME VOICES. 



Hidden fifths and octaves between the extreme voices are allowable, when the Allowable 
upper voice proceeds from one degree to the next above or below it. and octavea" 

between the 

Octaves. ex * reme 

voices. 



278. 




At the same time, it will be advisable that one of the accompanying voices 
should proceed in contrary motion or remain stationary, as at a, b, c. Ex. d, where 
all the parts proceed in similar motion, is therefore not so good. 

We may also here repeat what was said at page 18, namely, that hidden 
octaves are always preferable when the upper voice moves a semitone only. 

In the above examples it will be observed that the progression of hidden 
octaves is always towards the root of the chord. All those cases should be avoided 
in which the progression is towards the third ; for example : — 



279. 



P 



Bad. 



Bad. 



SE 



SE 



Preferable 
when the 
upper voice 
moves only 
one semitone. 

Hidden 
octaves pro- 
ceeding 
towards the 
third of thu 
chord. 



110 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE 



Towards the Even the progression of hidden octaves towards the fifth cannot be 

recommended. 



280. 



~7t ^^ — 


r-j 


Im '■> 




l(|J 


1 « U 



Objectionable Hidden fiftlis between the extreme voices are to be avoided when the upper 
hidden fifths J J tr 

between the voice proceeds by a leap, 
extreme 

voices. , , 

o. c. a. e. 



281. 



\ 



2C 



321 



sz: 



S3- 
rgr 



2£ 



322 



dS: 



Whenever the connection is rendered closer by means of a seventh, as at 
b, d, e, in the above example, the progression of the hidden fifth loses much 
of its harshness. 
Allowable Hidden octaves between the extreme voices are not unconditionally prohibited, 

hidden oc- , ,, . . , , , 

taves between when the upper voice proceeds by a leap. 

the extreme 
voices. 



282, 



I 



a. 



Not good. 
b. C 



Bad. 



2a: 



z? 



:C2~ 



^m 



=SF 



-^r=r 



^ 



~T3-" 



32" 

6 
32Z 



¥ 



-■m. 



Here also those progressions will be preferable in which the bass proceeds a 
semitone only, as at a. The remarks made on Ex. 279 and 280 will apply to 
examples d and e. 
Objectionable Hidden fifths and octaves between the extreme voices are to be avoided when 



atd^taTes 3 both voices proceed by a leap. 
between ex- 
treme voices. 



283. 




HIDDEN FIFTHS AND OCTAVES IN THE MIDDLE VOICES. 



Ill 



Such a progression as the above is however allowable, when formed by an -^ xce P*J on *° 
inversion of the same chord. rule. 



284. 



w— 


~^^-& 




: s> 


rJ — — - 


fr— 1 


m — o — 


o 






IS 


<s> J 




p-=^S 1 


1 ?-3 1 S 1 


Og? 


■&- 


P — | 




^^-"— 




r-j 






1 sr-^3 









HIDDEN FIFTHS AND OCTAVES IN THE MIDDLE VOICES. 

Although the progression of the middle voices ought to be as pure as that of 
the extreme voices, yet on account of their position, being as it were covered by 
the extreme parts, they may be allowed a greater freedom of progression, 
especially with regard to hidden fifths. 

Hidden octaves between the middle voices are seldom allowable, on account of Hidden fifths 
the voices becoming separated by too great a distance; and with respect to hidden between™ 8 
fifths, their good or bad effect will depend on the good connection of the chords middle voices. 
in other respects, and also upon their agreement with the rules relating to 
hidden fifths between extreme voices. 



285. 



-p 




3- 




1 S 




/l r -> 


<*j 




r^i 






m rzr 


. <s 




c=- — & 




_ r-J 


tr 


, ! "^ 


'j? - — 


. — -&- 


. - ..£2. 


/•v ^ " 




»"S 




S " 


r~- 


(££— 


*~~ ' 


rJ 




r'-* 




=* 















Bad. 



Bad. 



_iO. 



^S 



I£Zi 



m 



^Z22 



fe^ 



~-&r 



HIDDEN FD7THS AND OCTAVES BETWEEN AN EXTREME AND A MIDDLE 

VOICE. 



Here also the conditions under which such progressions may be employed, Between an 
cannot be determined by merely mechanical rules, but must depend on a ^ddL™' 1 



112 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



good and natural connection of the harmony. The following are a few 
examples : — 



•286. 




m 



=& 



~cr 



n 



gS a 



=& 



izz 



Not good Bad. 



■ r? 



Z22T 



3E 



3E 






zS=n 



rr?~ 



■St 



~g?~ 



Hidden One peculiar kind of hidden octave has still to be mentioned, namely, that 

passing over which passes over the seventh of a chord, when the seventh itself is already present 
of a chord. m an °ther voice (see page 59, Ex.144 b). This progression is always to be avoided. 



287. 



9 



I 



m 




fe 



3E 



s& 



-fea_ 



rS2i 



^g= 



2Z 



~rs~;. 



zzzz 



=& 



~trj- 



S 



ks>/»3 ^. 



* 



_ffi_ 



ESE 



I22T 



Hidden 
unisons. 



All that has been said of hidden octaves applies equally to hidden unisons. 



288. 



ZZ20T 



1 



Such progressions are forbidden between soprano, alto, and tenor, but may 
occur between tenor and bass, where they are to be treated as hidden octaves. 

Correction of We will now return to Ex. 273, in order to correct the faults it contains. 

Ezamp]e273. rr^g hidden fifth which there occurs between the fourth and fifth bar can 

however scarcely be remedied, since if we make the bass proceed in contrary 
motion, the same fault will appear in a different position, though it will be less 



HIDDEN FIFTHS AND OCTAVES IN THE MIDDLE VOICES. 



113 



perceptible on account of its occurring between an extreme and a middle voice, 
instead of between the extreme voices. 



289. 



I 



~v 


rj 


/\ <~j 








\\\f c "«j 






-s>- ^V 






if?)* 


/"J 




V. — "— 


"*" — -rzi — 





In such a case therefore we have no choice but to alter the harmony itself, 
and to make use of a different root, thus : — 

C F b° C _ d 7 G 7 C 



290, 



I 



& 



S 



^^r 



t£ff 



22" 



-d A 



=& 



22: 



8 7 



Or thus : — 



291. 



293. 



m 



w 



e 



221 



122: 



^ 



221 



-JL 



t3f 



22: 



221 



8 7 



Exercise. 





?h- 


G 


C 


G 


D 7 


G 


C 


G 


a 


D 7 


G 


292. \ 


fiir**- 




rj 


— s> — 


fj 


— — — 







. <*2 


rj 







m -i 










' — 










*--^ 



Defective accompaniment. 



fc 



2. 



3. 



4. 



it 



^ r 



~?7" 






22= 



EE 



— oo r j ' — 



22" 



221 



221 



8 7 



221 



Exercise in- 
correctly 
accompanied. 



The faults of the above example have been numbered for reference. 

The progression of the three upper voices by a leap upwards at No. 1 is not Progression 
good, since it deviates from all the rules of harmonic connection, and moreover is i ea p° 1CeS y * 
not necessary. 



114 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



The progression of one or two voices by a leap is only allowable when a third 
voice sustains the harmonic progression by remaining stationary or by moving in 
the contrary direction. 

The same fault is perceptible at No. 2, and is rendered still worse by the free 
entrance of both root and seventh. 



It has already been shown that either the dominant seventh or the root ought 

be prepared (see page 108). 

The following examples are therefore incorrect : — 



Free appear- 

and\eventh. to be prepared (see page 108). 



294. 




P 



ZE21 



E£ 



:?2j 



_C2_ 



m 



Jte- 



I 



Progressions similar to the above may however occasionally find an excuse in 
more important melodic rules. 

If the free entrance of root and seventh takes place in contrary motion, 
its effect, as has already been observed, is less unpleasant ; for example : — 



295. 



m 



::c7i 



321 



ZZ3Z 



ZE21 



<3-rr^-t-&-J&- 



321 



~^U 



•■n- 



Srz 



Progression 
by a leap of 
the bass of 

the chord of 



4. 



Example No. 293 also contains another fault at No. 2 — viz., a leap in the bass 
from the chord of 4 (see page 104). 

The third fault of Ex. No. 293 lies in the hidden fifth, which occurs between 
tenor and alto, and which is rendered more perceptible (because less hidden) by 
the leap of the soprano. 

The hidden fifth at No. 4 is objectionable, because it is not necessary ; that 
at No. 5 is, however, better, on account of the progression of both alto and bass 
being in contrary motion. 



HIDDEN FIFTHS AND OCTAVES IN THE MIDDLE VOICES. 115 

The following will therefore be the correct accompaniment of Ex. 293 • — 



296. 



I 



fc 



Eg 



es: 



ES 



m 



32=1 



.ca. 32. 32. 



=s A J. 



32; 



ZZZZ 



Exercises. 



P 



297. 



W=^= 



32; 



32; 



F Bt» — 



F C 7 



1 



2. 



. r? 



321 



3E 



£ 



G 



D 



G 



D 



D 



D 7 



G 



3. 



32T! 



GL 



~rzr 



321 



G 



D 



D 7 



G 



D 7 



G 



4. 



<z > 



32; 



^ 



G — 



D 



e 7 



D 



G D 7 



G 



P 



?F^P= 



327 



G 



D 7 



G 



G 



D 7 



P 



321 



P 



32; 



EfiE 



b° 



p 



8. 



321 



32; 



d»° 



The next exercise : — 



293. 



W- 



m°. 



116 HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 

with the following accompaniment : — 



299. 




=3= 



I£2I 



*\ 



22=q=2 



rpz 



i i I — 



J&. 



Ja_ 



The false 
relation. 



How avoided. 



Exceptions to 
the rule. 



contains an incorrect progression, known by the name of the false relation. 

The false relation, which belongs to the anti-melodic progressions, occurs 
when any note is immediately followed by the same note chromatically altered in 
another voice ; as in the second and third bars of the above example, where the 
G in the alto is immediately followed by the G $ in the bass. 

In order to avoid this fault the following rule must be observed : — 

When any note is to be immediately followed by the same note chromatically 
raised or lowered, such chromatic alteration must take place in one and the same 
voice. 

Although this rule is perfectly consistent with all the theoretical principles of 
harmony, there is perhaps none which admits of so many exceptions. The fol- 
lowing are a few of the examples of false relations which have no unpleasant 
effect : — 



300. 



M*±l£&k 



W^r^p 




Reason of the 
exceptions. 



In all these cases the false relation is not formed by essential notes of a simple 
harmonic progression, but is the result of a contraction or abridgment of certain 
natural progressions which, had they been employed in their complete form, 
would not have agreed with the metrical character of the phrase. 

The original progressions, by the contraction of which the above false 
relations were formed, are as follows : — 



301. 




THE FALSE RELATION. 



117 



These conditions, under which the false relation is allowable, are however not Objectionable 

false rela- 

contained in the following and similar examples, which are therefore incorrect : — tions. 

Or, 



302. 




With the false relations is also classed a progression known as the Tritone; this Progression of 

r D _ _ _ _ the tritone. 

is the progression of an augmented fourth, and is contained in the diatonic scale 
between the fourth and seventh degrees. It derives its name from the fact that 
it contains three whole tones : — 



303. 



I 



¥ 



-^=- 



~T2~ 



Like all augmented intervals, the tritone should be avoided on account of the Whyit should 
difficulty it presents to the singer. ' - 

This difficulty is doubtless caused by the fact that the two notes of which it is 
composed require two different resolutions — 



304. g^^j=fl 



of which one must be omitted if the interval be given to one voice, for example :— 



305. 



ife 



=st 



That this is however not the only reason of the unpleasant effect of the aug- Progression o 

mented fourth, is proved by its inversion, the diminished fifth, which would also cd'fifth'aliow 

require a two-fold resolution, but which is nevertheless constantly employed in its able * 
melodic form : — 



306. 



--&T- 



=t=* 



^L 



A 



The reason why the tritone has always been specially prohibited is that it 
was the only augmented interval which occurred in the simple harmonic progres- 
sions formerly in use. At the present time, however, it is merely classed with 



118 



HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



Different con- 
ditions under 
which the 
tritone ap- 
pears. 



the other augmented progressions, which in pure part-writing should be avoided 
as anti-melodic, or at least employed with the greatest caution. 

If the progression of the tritone is caused by an alteration of the position of 
one and the same chord, as at a in the following example, its appearance is not 
unexpected, and its effect much less unpleasant than when the notes of which it 
is composed belong to two different harmonies, as at b. 



307. 




Formerly the prohibition of the tritone was extended to the progression of 



Succession of 

two major 

thirds for- two consecutive major thirds, separated by the interval or a major second, tor 

merly for- , 

bidden. example :— 



308. p 



ES^S 



^m 



and it cannot be denied that in two parts this progression has the same unplea- 
sant effect as the tritone itself. In three or four parts, however, it is considerably 
less harsh. 



309. 




-£?" 



~C3" 



Correction of We now return to Ex. No. 299, in order to correct the false relation it 
Ex - m contains :- 



310. 




etc. 



HARMONIC ACCOMPANIMENT TO A GIVEN MIDDLE VOICE. 



119 



THE HARMONIC ACCOMPANIMENT TO A GIVEN MIDDLE VOICE. 

This exercise is extremely useful, aud cannot be begun too soon. As in the 
preceding examples, the roots which will serve as the foundations of the accom- 
panying harmonies will be indicated by means of letters. 



Cantus firmua 
in a middle 
voice. 



Exercise : — 
Alto. C 



311. 



P 



G 



In the alto. 



The progression of the bass will as usual be the most important, and should 
be considered first ; at the same time, however, the soprano may be added. 



Addition of 
soprano and 
bass. 



312. 



P 



&} 



73" 

G 



2Z: 



z=L 



G 



G 



C. 



ESE 



221 



22TT 



~?y~ 



22: 



TT 



The above phrase will be complete in three parts. With the addition of the 
tenor it will appear as follows : — 



Addition oi 
the tenor. 



313. 



ft 



zzzz^zzz. 



22; 



^T&— EC 



221 



22: 



-&- -<=- 



221 



-Z2I 



221 



^=A 



J dU. 



A given tenor will be similarly treated. 
Exercise : — 



314. 



5= 



221 



IUI 


C 


G 


a 


P 


C 


G 7 


C 


EH-? 


s s> 1 


r"J 


■ s> 






rj 




inR 































Cantus firm us 
in the tenoi. 



With addition of bass and soprano : — 



315. 






221 



~n~ 



221 



33: 



231 



J2. 



Accompanied 
by bass and 
Boprano. 



Addition of 
the alto. 



120 HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 

In four parts : — 



316. 



1 



W 



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Position of 
vuices. 



The student is reconunended to persevere in such exercises as the above 
until the progression of parts becomes perfectly pure and unconstrained. 

It may here be observed that in order to form a good four-part progression a 
good position of the voices is indispensable. The following rule with regard to 
position will be found serviceable. 

The distance which separates any two of the three upper voices must never 
exceed an octave. This ride, however, admits of exceptions as regards the 
relationship of tenor and bass to one another. 

The harmonic accompaniment of a given bass has been fully treated in 
the foregoing chapters on figured basses ; further consideration of this subject 
will therefore be unnecessary. 

Exercises. 

Alto given. 




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HARMONIC ACCOMPANIMENT TO A GIVEN MIDDLE VOICE 



121 



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HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. 



In the following exercises the roots have not been indicated, the choice of 
harmonies being left to the taste of the student. 



Exekcises. 
Soprano given. 



1. 



318. 
2. 





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CHAPTER XV. 
OF CADENCES. 



Different 
kinds of 
cadences. 



Their use. 



Employment 
of the plagal 
cadence at 
the end of a 
composition. 



Subdi visions 
of authentic 
cadences into 
perfect and 
imperfect. 

The perfect 
cadence. 



Various kinds of cadences have already been mentioned at different parts of 
this work, but we have not hitherto had an opportunity of considering them as 
fully as is necessary. We shall therefore proceed to do so in the present chapter. 

There are two principal kinds of cadences, the authentic and the plagal 
cadence : these are expressed by the following formulae, the authentic cadence by 
V-Ij and the plagal cadence by IV-I (or in minor by V-I and iv-l), as has 
already been shown. 

Both these kinds of cadences are used not only at the end of an entire com- 
position, but also for the close of certain sections thereof, such as periods, 
phrases, &c. 

This part of the subject belongs, however, to the theory of Composition; it 
will therefore be unnecessary to enter upon it here. 

When the plagal cadence is used at the end of a composition, it seldom 
appears alone, but is generally preceded by the authentic cadence, and then 
introduced by a modulation into the subdominant, thus : — 

Authentic Cadence. Plagal Cadence. 



319. 



The plagal cadence often closes a minor composition with the major chord, as 
in the above example. 

Authentic cadences are also subdivided into two kinds, viz., perfect and 
imperfect. 

The perfect authentic cadences are those in which the bass contains the roots 
of both the dominant and tonic chords, and in which the root of the chord of 
tonic is also contained in the soprano, for example : — 




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CADENCES. 



125 



If this is not the case, i. e., if either of the two chords be used in an inverted The imper- 
form, so that the root does not appear in the bass (as at a in the following example), 
or if the root of the chord of tonic be not contained in the soprano (as at b), the 
cadence is said to be imperfect. 



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PJUiAHitfL 

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322. 



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Another kind of cadence closing on the dominant, and expressed by the The send, 
formula I-V, is called the half-close or semi-cadence. 6U0e ° 



323. p= 



V. 

In the formation of the semi-cadence the chord of dominant may be preceded Other form* 
by other chords besides that of the tonic, for example : — eadenoe. 



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Certain modulations into the dominant, which are not effected by means of 
the dominant seventh, and the effect of which is undecided and transitory, may 
also be classed with the semi-cadences. 



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CADENCES. 



Examples 
of various 

cadcncw. 



In the following four-voiced chorale will be found examples of various 
cadences. The first line ends with a half-cadence, the second with a perfect 
cadence, the third with a plagal cadence in the relative major, the fourth with 
the same cadence in the original key, the fifth with a perfect cadence in the 
dominant of the relative major, and the sixth with a half-cadence in the 
original key. 

" Haupt voll Blut und Wunden." 



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INDEX 



n%:-** 



Accompaniment to a given voice, 102. 

Altered chords, 64. 

Alto, 11. 

Alto clef, 85. 

Anticipation, 90. 

Anti-melodic progressions, 105, 116. 

Augmented common chord, 24, 67. 

with seventh added, 68. 

Augmented fourth, 20, 49, 117. 

intervals, 65. 

second, 25, 27. 

sixth, chord of, 70. 

sixth and fifth, chord of, 71. 

sixth, fourth, and third, chord of, 70. 

Bass, 10. 

harmonic accompaniment of, 120. 

progression of, 103. 

Cadence, 16, 22, 33, 99, 124. 

deceptive, 60, 125. 

Cantus firmus, 102, 119. 
Chorale, 126. 
Chords, 9. 

major and minor, 9. 

of the seventh, connection of, 51. 

secondary, 16, 24. 

Chromatic alteration of chords, 64. 

scale, 3. 

Clefs, vocal, 84. 
Consecutive fifths, 12, 72, 82. 

fifths, allowable, 32. 

octaves, 12, 82. 

Consonances, perfect and imperfect, 5. 
Contrary motion, 12. 

Covered fifths, 14, 18, 108. 
octaves, 14, 18, 33, 59, 108. 

Deceptive cadence, 60, 125. 
Degrees of the scale, 1. 
Diminished fifth, 41', 65, 67. 

, chord of, 44. 

intervals, 65. 

seventh, chord of, 44, 96. 

Dissonances, 5. 

Dominant, chord of, 10, 94. 

in minor, 23. 

seventh, 35, 50, 95, 108, 114. 

Doubly-diminished chord, 70. 

Eleventh, chord of, 62. 



Enharmonic modulation, 97. 

Exercises — On the common chords of the major 
scale, 14, 19 ; On the common chords of 
the minor scale, 26 ; On the inversions of 
the common chords, 31 ; On the chord of 
the seventh, 38 ; On the inversions of the 
chord of the seventh, 42 ; On the secon l- 
ary sevenths, 50, 51, 54, 61 ; On the in- 
versions of the secondary sevenths, 56 ; On 
the deceptive cadence, 60 ; On alter d 
chords, 69, 72 ; On modulations, 77 ; On 
suspensions, 83, 89 ; On the harmonic 
accompaniment to a given soprano, 107, 
115, 122; On the harmonic accompani- 
ment to a given alto, 120, 122 ; On the 
harmonic accompaniment to a given tenor 
121, 123. 

Extreme voices, 11. 

hidden fifths and octaves between, 109. 

False relation, 116. 
Fifths, 4. 

augmented, 24, 65, 67. 

consecutive, 12, 32, 72, 82. 

diminished, 19, 41, 65, 67. 

hidden, 14, 18, 108. 

Figuring of chords, 26, 29, 34, 35, 40. 

of suspensions, 83. 

Fourth, 4. 

augmented, 20. 

French sixth, 71. 

German sixth, 71. 

Half close, 125. 

Harmonic accompaniment, 102. 

Harmony, close and extended, 14. 

Hidden fifths, 14, 18, 108. 

Hidden octaves, 14, 18, 33, 59, 108. 

Imperfect cadence, 125. 
Inganno, 60, 125. 
Intervals, 3. 

augmented and diminished, 65 

consonant and dissonant, 5. 

major and perfect, 4. 

minor, 5. 

Italian sixth, 70. 

Inversion of common chords, 29. 

of intervals, 6. 

of secondary sevenths, 55. 



128 



INDEX. 



of the augmented chord, 68. 

of the chord of diminished fifths, 31. 

of the chord of the seventh, 40. 

Leading note, 20, 36, 53, 87. 

chord of the seventh on the, 47, 53. 

Major and minor scales, 2. 

intervals, 5. 

chords, 9. 

Major Scale, chords of the, 9. 

Middle voice, accompaniment to a, 119. 

Middle voices, 11. 

hidden fifths and octaves between, 11. 

Minor scale, chords of the, 23. 
Modulation, 76, 93. 
Modulation enharmonic, 97. 

extended, 99. 

Motion, similar, contrary, and oblique, 12. 

Ninth, chord of the, 62, 72, 88. 

Oblique motion, 12. 
Octave, 4. 

augmented and diminished, 65, 

Octaves, consecutive, 12, 82. 
hidden, 14, 18, 33, 59, 108. 

Passing notes, 90. 
Passing seventh, 81. 
Perfect cadence, 124. 
Plagal cadence, 16, 124. 

in minor, 23. 

Position of voices, 15, 30, 31, 120. 
Preparation of the ninth, 62. 

of the seventh, 49. 

of the sixth and fourth, 103. 

of the suspension, 79. 

Relative scales, 3. 

Resolution — Of augmented and diminished 
intervals, 20 ; Of the leading note, 20 ; 
Of the chord of diminished fifth, 21, 32 ; 
Of the augmented fourth, 32 ; Of the 
dominant seventh, 36 ; Of the chord of 
the sixth and fifth, 40 ; Of the chord of 
the sixth, fourth, and third, 41 ; Of the 
chord of the sixth, fourth, and second, 41 ; 
Of the secondary sevenths, 46 ; Of the 
chord of the seventh on the leading 
note, 47 ; Of the diminished seventh, 53, 
61 ; Of the inversions of the secondary 
sevenths, 55 ; Of the seventh (free), 75 ; 
Of the augmented chord, 67 ; Of the 
augmented sixth, 70 ; Of the augmented 
sixth, fourth, and third, 71 ; Of the 
augmented sixth and fifth, 71 ; Of the 
suspension, 81 , 88. 

Retardation, 87. 



Scale, chromatic, 3. 

diatonic major,l. 

minor, 2. 

Score, vocal, 86. 
Second, 4. 

augmented, 25, 27, 65. 

Second major and minor, 5. 
Semi-cadence, 125. 
Semitones, 1. 
Sequence, 19. 

of sixths, 33. 

Seventh, 4 

chord of, 35. 

combined with the augmented chord, 68. 

diminished, 44, 53, 65, 96. 

dominant, 35, 50, 95, 108, 114. 

on the leading note, 47. 

secondary chords of, 44. 

secondary, in minor, 52. 

Similar motion, 12. 
Sixth, 4. 

major and minor, 5. 

augmented, 65, 

augmented, chord of, 70. 

chord of, 29. 

and fifth, chord of, 49. 

and fourth, chord of, 29, 33, 88, 95, 97, 

103, 114. 

fourth and second, chord of, 40. 

fourth and third, chord of, 40. 

Soprano, 10. 
Soprano clef, 85. 

harmonic accompaniment of, 102. 

Subdominant, chord of, 10. 
Suspensions, 63, 78, 104. 
double, 88. 

Table of all the chords, 73 

of common chords, 28. 

■ of inversions, 7, 66. 

of resolutions of the inversions of the 

dominant seventh, 42. 
Tenor, 11. 

clef, 85. 

Third, 4. 

diminished, 65. 

major and minor, 5. 

major, succession of, 118. 

Thirteenth, chord of, 62. 
Tone, 1 . 

Tonic, chord of, 10, 94. 
Tritone, 20,49, 117. 

Unison, 4. 

augmented, 65. 

Unisons, hidden, 112. 



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